graph theory master thesis

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Bessy, Stéphane. "Some problems in graph theory and graphs algorithmic theory." Habilitation à diriger des recherches, Université Montpellier II - Sciences et Techniques du Languedoc, 2012. http://tel.archives-ouvertes.fr/tel-00806716.

Myers, Joseph Samuel. "Extremal theory of graph minors and directed graphs." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619614.

Johnson, Chase R. "Molecular Graph Theory." Digital WPI, 2010. https://digitalcommons.wpi.edu/etd-theses/1179.

Feghali, Carl. "Topics in graph colouring and extremal graph theory." Thesis, Durham University, 2016. http://etheses.dur.ac.uk/11790/.

Nikwigize, Adolphe. "Graph theory : Route problems." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-17397.

Berg, Deborah. "Connections Between Voting Theory and Graph Theory." Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/178.

Hatt, Justin Dale. "Online assessment of graph theory." Thesis, Brunel University, 2016. http://bura.brunel.ac.uk/handle/2438/13389.

Keevash, Peter. "Topics in extremal graph theory." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619938.

Law, Ka-ho, and 羅家豪. "Some results in graph theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44899816.

Morrison, Julie Lindsay. "Computational graph theory in bioinformatics." Thesis, University of Strathclyde, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435114.

Richer, Duncan Christopher. "Graph theory and combinatorial games." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621916.

Eggemann, Nicole. "Some applications of graph theory." Thesis, Brunel University, 2009. http://bura.brunel.ac.uk/handle/2438/3953.

Nieh, Ari. "Fractional Analogues in Graph Theory." Scholarship @ Claremont, 2001. https://scholarship.claremont.edu/hmc_theses/131.

Reed, Bruce. "A semi-strong perfect graph theorem /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72812.

Letzter, Shoham. "Extremal graph theory with emphasis on Ramsey theory." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709415.

Meek, Darrin Leigh. "On graph approximation heuristics : an application to vertex cover on planar graphs." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/24088.

Zuffi, Lorenzo. "Simplicial Complexes From Graphs Toward Graph Persistence." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13519/.

Anderson, Jon K. "Genetic algorithms applied to graph theory." Virtual Press, 1999. http://liblink.bsu.edu/uhtbin/catkey/1136714.

Peng, Richard. "Algorithm Design Using Spectral Graph Theory." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/277.

Islam, Mustafa R. "A hypertext graph theory reference system." Virtual Press, 1993. http://liblink.bsu.edu/uhtbin/catkey/879844.

Edwards, C. S. "Some extremal problems in graph theory." Thesis, University of Reading, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373467.

Garbe, Frederik. "Extremal graph theory via structural analysis." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8869/.

Grinshpun, Andrey Vadim. "Some problems in Graph Ramsey Theory." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/97767.

Pappone, Francesco. "Graph neural networks: theory and applications." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23893/.

Parks, David J. "Graph theory in America, 1876-1950." Thesis, Open University, 2012. http://oro.open.ac.uk/54663/.

Schuerger, Houston S. "Contributions to Geometry and Graph Theory." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1707341/.

Weaver, Robert Wooddell. "Some problems in structural graph theory /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487268021746449.

Florkowski, Stanley F. "Spectral graph theory of the Hypercube." Thesis, Monterey, Calif. : Naval Postgraduate School, 2008. http://edocs.nps.edu/npspubs/scholarly/theses/2008/Dec/08Dec%5FFlorkowski.pdf.

Han, Lin. "Graph generative models from information theory." Thesis, University of York, 2012. http://etheses.whiterose.ac.uk/3726/.

Robinson, Laura Ann. "Graph Theory for the Middle School." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2226.

Loveland, Susan M. "The Reconstruction Conjecture in Graph Theory." DigitalCommons@USU, 1985. https://digitalcommons.usu.edu/etd/7022.

Yi, Peipei. "Graph query autocompletion." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/557.

Hegde, Rajneesh. "New Tools and Results in Graph Structure Theory." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10481.

Lopez, Christian P. "On the relationship between a graph and the cycle graph of its complement." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 1995. https://ro.ecu.edu.au/theses/1184.

Morisi, Rita. "Graph–based techniques and spectral graph theory in control and machine learning." Thesis, IMT Alti Studi Lucca, 2016. http://e-theses.imtlucca.it/188/1/Morisi_phdthesis.pdf.

Hoang, Chinh T. "Perfect graphs." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74011.

Hayward, Ryan B. "Two classes of perfect graphs." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74025.

Olariu, Stephan. "Results on perfect graphs." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=73997.

Waterhouse, Mary Alexandra Paula Royston Hastilow. "Coloured graph decompositions /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18769.pdf.

Weinstein, Lee. "Empirical study of graph properties with particular interest towards random graphs." Diss., Connect to the thesis, 2005. http://hdl.handle.net/10066/1485.

Narayanan, Bhargav. "Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/252850.

Fiala, Nick C. "Some topics in combinatorial design theory and algebraic graph theory /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486402957198077.

Burns, Jonathan. "Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5193.

Turner, Bethany. "Embeddings of Product Graphs Where One Factor is a Hypercube." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/2455.

Srikanthan, T. "Bond graph analysis." Thesis, Coventry University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373896.

Chen, Xujin, and 陳旭瑾. "Graph partitions and integer flows." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30286256.

Vella, Antoine. "A Fundamentally Topological Perspective on Graph Theory." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1033.

Douma, Femke. "Counting and averaging problems in graph theory." Thesis, Durham University, 2010. http://etheses.dur.ac.uk/272/.

Al-Shimary, Abbas. "Applications of graph theory to quantum computation." Thesis, University of Leeds, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608359.

Yilma, Zelealem Belaineh. "Results in Extremal Graph and Hypergraph Theory." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/49.

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Home > Graduate College > Theses > 957

Masters Theses

Graph theory based routing algorithms, date of award, degree name.

Master of Science

Computer Science

First Advisor

Dr. Naveed A. Sherwani

Second Advisor

Dr. Fred Boals

Third Advisor

Dr. Ajay Gupta

Access Setting

Masters Thesis-Open Access

In this thesis, we study two VLSI layout problems.

We investigate the Minimum-Bend Single Row Routing Problem in which the objective function is to minimize the number of doglegs (or blends) per net. Our approach uses a graph theoretic representation in which an instance of the Single Row Routing Problem is represented by three graphs, an overlap graph, a containment graph and an interval graph. Using this graph representation, we develop three algorithms for minimum-bend single row routing problem.

We present a three-layer over-the-cell router (ICR-3) for the standard cell design style based on a new cell model which assumes that terminals are located in the center of the cells in layer M2. This model is similar to the one currently being developed for three-layer cell libraries in industry. We have implemented ICR-3 in C on a SUN SPARCstation 1+ and tested it on several benchmarks including PRIMARY I and PRIMARY II from MCNC. We show that ICR-3 produces results which are better (on the average) by 58% as compared to a two layer over-the-cell (2OTC) router and 47% as compared to a conventional three layer channel (3CRP) router. (Abstract shortened with permission of author.)

Recommended Citation

Wu, Bo, "Graph Theory Based Routing Algorithms" (1992). Masters Theses . 957. https://scholarworks.wmich.edu/masters_theses/957

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BS-MS Thesis: Graph Theory of Sudoku

This project aims to study and contribute to a clear and rigorous un- derstanding of mathematics behind the popular number placement puzzle - Sudoku. Sudoku puzzle consists of a 9 × 9 grid of 81 cells (or slots) with some cells already filled with digits from 1 to 9. The objective of the puzzle is to fill the rest of the grid with digits from 1 to 9 such that no digit repeats within any row, column and specified 3 × 3 blocks. For anyone trying to solve a Sudoku puzzle, several questions arise naturally. To cite a few: for a given puzzle, does a solution exist? If the solution exists, is it unique? If the solution is not unique, how many solutions are there? Moreover, is there a systematic way of determining all the solutions? How many puzzles are there with a unique solution? What is the minimum number of initial entries that can be specified in a single puzzle in order to ensure a unique solution? This project attempts to answer such interesting and intriguing questions. Many of the above questions have been addressed in the paper Sudoku Squares and Chromatic Polynomials by Agnes M. Herzberg and M. Ram Murty published in Notices of the American Mathematical Society Vol- ume 54 Issue 6 in June/July 2007. [5] This project report provides a detailed study of Agnes M. Herzberg and M. Ram Murty’s paper filling all its gaps and in the process gives an elaborate introduction to all mathematical concepts encountered. Since Sudoku is a special case of a general graph theoretic problem (as will be shown in the report), concepts and insights involving graph theory are emphasized using Frank Harary’s book on Graph Theory [4]. In addition some applications of these concepts are demonstrated.

Related Papers

"Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)"

Lenox Institute

Tsao, Hung-ping (2022). The Natural Sudoku Lecture 1. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 11A, November 2022; 66 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL4-NUM11A-NOV2022; ISBN 978-0-9890870-3-2. https://doi.org/10.17613/mwvw-kp81 ........ABSTRACT: (a) Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used. (b) We shall give only three examples. (PLC will be used none in the first and 7 times in the second, which took a Finnish mathematician Arto Inkala three months to design and posted online in 2012. I was the first one to solve it manually in the total of ten hours. I will show you here how it can be solved in twenty minutes by using PLC. The third one has twelve different solutions!) (c) This lecture serves as the preface for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing two puzzles with illustrative solutions, the second one of which is the demonstration of the first of the 49 practice puzzles with annotated solutions. All natural Sudoku puzzles are downloaded from Gordon Royle list. (d) The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for our insuing lectures. (e) The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple solutions in the collection of practice sets for you. (f) The lectures are presented in the power point format, convenient for any interested instructors to use.

Tsao, Hung-ping (2022). The Natural Sudoku Lecture 2. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 11B, November 2022; 62 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL4-NUM11B-NOV2022; ISBN 978-0-9890870-3-2. https://doi.org/10.17613/vanr-qw78 ....ABSTRACT:(a)Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used; (b)We shall give only three examples. (PLC will be used none in the first and 7 times in the second, which took a Finnish mathematician Arto Inkala three months to design and posted online in 2012. I was the first one to solve it manually in the total of ten hours. I will show you here how it can be solved in twenty minutes by using PLC. The third one has twelve different solutions!); (c)This lecture serves as the preface for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing two puzzles with illustrative solutions, the second one of which is the demonstration of the first of the 49 practice puzzles with annotated solutions. All natural Sudoku puzzles are downloaded from Gordon Royle list; (d) The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for our insuing lectures; (e) The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple solutions in the collection of practice sets for you; and (f) The lectures are presented in the power point format, convenient for any interested instructors to use.

Lawrence K . Wang

Tsao, Hung-ping (2023). The Natural Sudoku Lecture 10. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 5, NUMBER 9A, September 2023; 58 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL5-NUM9A-SEP2023; ISBN 978-0-9890870-3-2. Doi.org/10.17613/dc30-wg05 ...... ABSTRACT: Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used. This lecture serves as the preface for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing two puzzles with illustrative solutions, the second one of which is the demonstration of the first of the 49 practice puzzles with annotated solutions. All natural Sudoku puzzles are downloaded from Gordon Royle list. The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for any of our lectures. Hard puzzles can sometimes be solved by the construction of strategic flipflops. The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple or no solutions in the collection of practice sets for you. The lectures are presented in the power point format, convenient for any interested instructors to use.

Tsao, Hung-ping (2022). The Natural Sudoku Lecture 4. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 11D, November 2022; 60 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL4-NUM11D-NOV2022; ISBN 978-0-9890870-3-2. Doi.org/10.17613/p2v6-cz17 ..... ABSTRACT: (a) Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used; (b) This lecture serves as the preface for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing two puzzles with illustrative solutions, the second one of which is the demonstration of the first of the 49 practice puzzles with annotated solutions. All natural Sudoku puzzles are downloaded from Gordon Royle list; (c) The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for any of our lectures; (d) The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple or no solutions in the collection of practice sets for you; and (e)The lectures are presented in the power point format, convenient for any interested instructors to use.

Tsao, Hung-ping (2022). The Natural Sudoku Lecture 8. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, NUMBER 11I, November 2022; 61 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL4-NOV11I-2022; ISBN 978-0-9890870-3-2. Doi.org/10.17613/p184-kf67 ......... ABSTRACT: (a) Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used; (b) This lecture serves as the preface for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing two puzzles with illustrative solutions, the second one of which is the demonstration of the first of the 49 practice puzzles with annotated solutions. All natural Sudoku puzzles are downloaded from Gordon Royle list; (c) The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for any of our lectures;(d) The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple or no solutions in the collection of practice sets for you; (e) The lectures are presented in the power point format, convenient for any interested instructors to use; (f) The solving process of each and every natural Sudoku puzzle is, in deed, performing in an act of martial art as well as poetic rhythm; and (g) Translation of a poem of Yang Shen (楊慎 臨江仙) is attached in the appendix (and more).

Tsao, Hung-ping (2022). The Natural Sudoku Lecture 4. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 11E, November 2022; 58 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL4-NUM11E-NOV2022; ISBN 978-0-9890870-3-2. Doi.org/10.17613/gg8e-mq58 .... ABSTRACT: (a) Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used; (b) This lecture serves as the preface for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing two puzzles with illustrative solutions, the second one of which is the demonstration of the first of the 49 practice puzzles with annotated solutions. All natural Sudoku puzzles are downloaded from Gordon Royle list; (c) The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for any of our lectures; (d) The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple or no solutions in the collection of practice sets for you; and (e) The lectures are presented in the power point format, convenient for any interested instructors to use.

Tsao, Hung-ping (2022). The Natural Sudoku Lecture 6. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 11G, November 2022; 66 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL4-NOV11G-2022; ISBN 978-0-9890870-3-2. Doi.org/10.17613/ajww-bg71 ..... ABSTRACT: (a) Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used; (b)This lecture serves as the preface for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing two puzzles with illustrative solutions, the second one of which is the demonstration of the first of the 49 practice puzzles with annotated solutions. In this lecture, we shall introduce the construction of strategic flipflops to solve both puzzles.All natural Sudoku puzzles are downloaded from Gordon Royle list; (c) The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for any of our lectures. Hard puzzles can sometimes be solved by the construction of strategic flipflops; (d) The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple or no solutions in the collection of practice sets for you; and (e) The lectures are presented in the power point format, convenient for any interested instructors to use.

(a) Hard sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used; (b) This lecture serves as the preface for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing two puzzles with illustrative solutions, the second one of which is the demonstration of the first of the 49 practice puzzles with annotated solutions. All natural Sudoku puzzles are downloaded from Gordon Royle list; (c) The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for any of our lectures. Hard puzzles can sometimes be solved by the construction of strategic flipflops; (d) The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple or no solutions in the collection of practice sets for you; (e) The lectures are presented in the power point format, convenient for any interested instructors to use; and (f) Mini Martial Art Fiction is attached in the appendix.

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Marc Càmara . Algebraic and Combinatoric Approach to Pseudo-distance Regularity and Completely Pseudo-regular Codes . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jun. 2011.

Jordi Moragas . Graph Labelings and Decompositions by Partitioning Sets of Integers . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jun. 2010.

Diego González . Fault Tolerance Results for Some Families of Graphs . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Nov. 2009.

Ignasi Sau . Optimization of Graphs under Degree Constraints: Application to Telecommunication Networks . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Oct. 2009.

Amanda Montejano . Colored Combinatorial Structures: Homomorphisms and Counting . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jun. 2009.

Cristina Dalfó . Estudi i Disseny de Grans Xarxes d'Interconnexió: Modularitat i Comunicació . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Des. 2007.

Javier Barajas. Coloring Problems in Cayley Graphs . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jun. 2007.

Silvia Gago. Métodos espectrales y nuevas medidas, modelos y parámetros en grafos pequeño-mundo invariantes de escala . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jul. 2006.

Christian Barrientos. Difference Graph Labelings. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jul. 2004.

Eduardo Canale. Estudio y construcción de estructuras topológicas idóneas para la modelización de redes de interconexión. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Abr. 2003.

Xavier Marcote. Some Contributions to the Study of the Connectedness of Graphs and Digraphs. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Abr. 2003.

Susana C. López Masip. Descomposicions de grafs en arbres . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Feb. 2003.

Francesc A. Muntaner. Magic Graphs . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Nov. 2001.

Javier Ozón. Contribución al coloreado de grafos y las redes pequeño-mundo . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jul. 2001.

Sonia Pérez. Recubrimientos k-arco transitivos de digrafos . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Feb. 2001.

Montserrat Maureso. Digrafs sobre grups abelians finits: anàlisi dels digrafs endo-circulants. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jun. 2000.

Iñaki Pelayo. Some contributions from Graph Theory to the design and study of Large and Fault-tolerant Interconnection Networks . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Abr. 2000.

Joan Gimbert. Aplicacions de la Teoria Espectral a l'Estudi dels Digrafs Densos. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Abr. 2000.

Amauri Gutiérrez. Descomposiciones de grafos regulares. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Feb. 2000.

Lali Barrière. Anells cordals: propietats estructurals i models de comunicacions. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Oct. 1999.

Daniela Ferrero. Graphs and hypergraphs as interconnection network models. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jul. 1999.

Margarida Mitjana. Propagació d'informació en grafs i digrafs que modelen xarxes d'interconnexió simètriques. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Mar. 1999.

Ernest Garriga. Contribució a la Teoria Espectral de Grafs.Problemes mètrics i distància-regularitat . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Dec. 1997.

Juan Alberto Rodríguez. Cotas de Diversos Parámetros de un Grafo a partir de los Autovalores de su Matriz Laplaciana. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jul. 1997.

Xavier Muñoz. Digrafs linia. Alguns aspectes en comunicacions. (Broadcasting i vulnerabilitat) . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Des. 1996.

Camino Balbuena. Estudio sobre algunas nuevas clases de conectividad condicional en grafos dirigidos . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Nov. 1995.

Angeles Carmona. Grafos y digrafos con máxima conectividad y máxima distancia conectividad . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Nov. 1995.

E. Simó. Vulnerabilidad del diámetro de ciertas familias de grafos . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Jul. 1995.

M. Espona. Xarxes de Permutacions i Digrafs Acolorits: Anàlisi i Disseny. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Dec. 1994.

J. Gómez. Contribución a la Teoria de Grafos Densos. Doctoral Thesis, Univ. Autònoma de Barcelona, Barcelona, 1994.

J.M. Brunat. Contribució a l'estudi de la simetria de grafs dirigits i les seves aplicacions . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Oct. 1994.

J.L. Villar. Contribución a la Teoría de Redes con Enlaces Bidireccionales Derivadas de los Digrafos L\' \i nea . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Nov. 1994.

M. Zaragozà. Redes de Interconexión: Contribución al Estudio de su Vulnerabilidad . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1994.

F. Aguiló. Caracterització i Disseny de les Xarxes d'Interconnexió de Doble Llaç Óptimes . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1994.

Carles Padró. Vulnerabilitat en Famílies Óptimes de Digrafs per al Disseny de Xarxes d'Interconnexió . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1994.

F. Hurtado. Problemas de Visibilidad Geomètrica . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1993.

A. S. Lladó. Contribució a l'Estudi i al Diseny de Xarxes d'Interconexió amb Enllaços Unidireccionals . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1989.

M. Mora. Digrafs c-Circulants com a Model per a Xarxes d'Interconnexió . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1988.

O. Serra. Models Algèbrics per a Emmagatzament de Dades . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1988.

P. Morillo. Grafos y Digrafos Asociados con Teselaciones como Modelos para Redes de Interconexión . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1987.

M. Escudero. Contribución al Estudio de Redes Modeladas por Grafos sobre Alfabeto . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1987.

J. Gómez. Diámetro y Vulnerabilidad en Redes de Interconexión . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1986.

J. Fàbrega. Grafos y Redes de Interconexión: Diseño, Fiabilidad y Encaminamiento. Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, Sep. 1984.

M.A. Fiol. Aplicaciones de la Teoria de Grafos al Diseño de Redes de Interconexión de Multiprocesadores . Doctoral Thesis, Univ. Politècnica de Catalunya, Barcelona, 1982.