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Rozprawy doktorskie na temat „Graph theory”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

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.

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This document is a long abstract of my research work, concerning graph theory and algorithms on graphs. It summarizes some results, gives ideas of the proof for some of them and presents the context of the different topics together with some interesting open questions connected to them The first part precises the notations used in the rest of the paper; the second part deals with some problems on cycles in digraphs; the third part is an overview of two graph coloring problems and one problem on structures in colored graphs; finally the fourth part focus on some results in algorithmic graph the

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2

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.

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3

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

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Graph Theory is a branch of mathematics that has a wealth of applications to other science and engineering disciplines, specifically Chemistry. The primary application of graphs to Chemistry is related to understanding of structure and symmetry at the molecular level. By projecting a molecule to the plane and examining it as a graph, a lot can be learned about the underlying molecular structure of a given compound. Using concepts of Graph Theory this masters project examines the underlying structures of two specific families of compounds, fullerenes and zeolites, from a chemical and mathematic

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4

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

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In this thesis we consider three problems related to colourings of graphs and one problem in extremal graph theory. Let $G$ be a connected graph with $n$ vertices and maximum degree $\Delta(G)$. Let $R_k(G)$ denote the graph with vertex set all proper $k$-colourings of $G$ and two $k$-colourings are joined by an edge if they differ on the colour of exactly one vertex. Our first main result states that $R_{\Delta(G)+1}(G)$ has a unique non-trivial component with diameter $O(n^2)$. This result can be viewed as a reconfigurations analogue of Brooks' Theorem and completes the study of reconfigurat

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5

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.

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6

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

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Mathematical concepts have aided the progression of many different fields of study. Math is not only helpful in science and engineering, but also in the humanities and social sciences. Therefore, it seemed quite natural to apply my preliminary work with set intersections to voting theory, and that application has helped to focus my thesis. Rather than studying set intersections in general, I am attempting to study set intersections and what they mean in a voting situation. This can lead to better ways to model preferences and to predict which campaign platforms will be most popular. Because I

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7

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

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The objective of this thesis is to establish whether or not online, objective questions in elementary graph theory can be written in a way that exploits the medium of computer-aided assessment. This required the identification and resolution of question design and programming issues. The resulting questions were trialled to give an extensive set of answer files which were analysed to identify whether computer delivery affected the questions in any adverse ways and, if so, to identify practical ways round these issues. A library of questions spanning commonly-taught topics in elementary graph t

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8

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

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9

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.

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10

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

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11

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

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12

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

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13

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

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Tait showed in 1878 that the Four Color Theorem is equivalent to being able to three-color the edges of any planar, three-regular, two-edge connected graph. Not surprisingly, this equivalent problem proved to be equally difficult. We consider the problem of fractional colorings, which resemble ordinary colorings but allow for some degree of cheating. Happily, it is known that every planar three-regular, two-edge connected graph is fractionally three-edge colorable. Is there an analogue to Tait’s Theorem which would allow us to derive the Fractional Four Color Theorem from this edge-coloring re

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14

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.

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15

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.

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16

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.

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17

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

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Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph

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18

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

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This thesis proposes two new variations on the genetic algorithm. The first attempts to improve clustering problems by optimizing the structure of a genetic string dynamically during the run of the algorithm. This is done by using a permutation on the allele which is inherited by the next generation. The second is a multiple pool technique which ensures continuing convergence by maintaining unique lineages and merging pools of similar age. These variations will be tested against two well-known graph theory problems, the Traveling Salesman Problem and the Maximum Clique Problem. The results wil

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19

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

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Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. Laplace’s equation and its discrete form, the Laplacian matrix, appear ubiquitously in mathematical physics. Due to the recent discovery of very fast solvers for these equations, they are also becoming increasingly useful in combinatorial optimization, computer vision, computer graphics, and machine learning. In this thesis, we develop highly efficient and parallelizable algorithms for solving linear systems involving graph Laplacian matrices. These solvers can also be extended to symmetric diagonally

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20

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

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G-Net system is being developed by the members of the G-Net research group under the supervision of Dr. K. Jay Bagga. The principle objective of the G-Net system is to provide an integrated tool for dealing with various aspects of graph theory. G-Net system is divided into two parts. GETS (Graph theory Experiments Tool Set) will provide a set of tools to experiment with graph theory, and HYGRES (HYpertext Graph theory Reference Service), the second subcomponent of the G-Net system to aid graph theory study and research. In this research a hypertext application is built to present the graph the

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21

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.

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22

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

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We discuss two extremal problems in extremal graph theory. First we establish a precise characterisation of 4-uniform hypergraphs with minimum codegree close to n/2 which contain a Hamilton 2-cycle. As a corollary we determine the exact Dirac threshold for Hamilton 2-cycles in 4-uniform hypergraphs, and we provide a polynomial-time algorithm which answers the corresponding decision problem for 4-graphs with minimum degree close to n/2. In contrast we also show that the corresponding decision problem for tight Hamilton cycles in dense k-graphs is NP-complete. Furthermore we study the following

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23

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

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 149-156).<br>A graph G is r-Ramsey minimal with respect to a graph H if every r-coloring of the edges of G yields a monochromatic copy of H, but the same is not true for any proper subgraph of G. The study of the properties of graphs that are Ramsey minimal

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24

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

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Le reti neurali artificiali hanno visto, negli ultimi anni, una crescita vertiginosa nelle loro applicazioni e nelle architetture dei modelli impiegati. In questa tesi introduciamo le reti neurali su domini euclidei, in particolare mostrando l’importanza dell’equivarianza di traslazione nelle reti convoluzionali, e introduciamo, per analogia, un’estensione della convoluzione a dati strutturati come grafi. Inoltre presentiamo le architetture dei principali Graph Neural Network ed esponiamo, per ognuna delle tre architetture proposte (Spectral graph Convolutional Network, Graph Co

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25

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

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This narrative is a history of the contributions made to graph theory in the United States of America by American mathematicians and others who supported the growth of scholarship in that country, between the years 1876 and 1950. The beginning of this period coincided with the opening of the first research university in the United States of America, The Johns Hopkins University (although undergraduates were also taught), providing the facilities and impetus for the development of new ideas. The hiring, from England, of one of the foremost mathematicians of the time provided the necessary motiv

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26

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

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In geometry we will consider n-dimensional generalizations of the Power of a Point Theorem and of Pascal's Hexagon Theorem. In generalizing the Power of a Point Theorem, we will consider collections of cones determined by the intersections of an (n-1)-sphere and a pair of hyperplanes. We will then use these constructions to produce an n-dimensional generalization of Pascal's Hexagon Theorem, a classical plane geometry result which states that "Given a hexagon inscribed in a conic section, the three pairs of continuations of opposite sides meet on a straight line." Our generalization of this

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27

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

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28

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.

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Thesis (M.S. in Applied Mathematics)--Naval Postgraduate School, December 2008.<br>Thesis Advisor(s): Rasmussen, Craig W. "December 2008." Description based on title screen as viewed on January 29, 2009. Includes bibliographical references (p. 51-52). Also available in print.

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29

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

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Generative models are commonly used in statistical pattern recognition to describe the probability distributions of patterns in a vector space. In recent years, sustained by the wide range of mathematical tools available in vector space, many algorithms for constructing generative models have been developed. Compared with the advanced development of the generative model for vectors, the development of a generative model for graphs has had less progress. In this thesis, we aim to solve the problem of constructing the generative model for graphs using information theory. Given a set of sample gr

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30

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

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After being introduced to graph theory and realizing how it can be utilized to solve real-world problems, the author decided to create modules of study on graph theory appropriate for middle school students. In this thesis, four modules were developed in the area of graph theory: an Introduction to Terms and Definitions, Graph Families, Graph Operations, and Graph Coloring. It is written as a guide for middle school teachers to prepare teaching units on graph theory.

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31

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

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In this paper we show that specific classes of graphs are reconstructible; we explore the relationship between the. reconstruction and edge-reconstruction conjectures; we prove that several classes of graphs are actually Harary to the reconstructible; and we give counterexamples reconstruction and edge-reconstruction conjectures for infinite graphs.

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32

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

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The prevalence of graph-structured data in modern real-world applications has led to a rejuvenation of research on graph data management and analytics. Several database query languages have been proposed for textually querying graph databases. Unfortunately, formulating a graph query using any of these query languages often demands considerable cognitive effort and requires "programming" skill at least similar to programming in SQL. Yet, in a wide spectrum of graph applications consumers need to query graph data but are not proficient query writers. Hence, it is important to devise intuitive t

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33

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.

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From an arbitrary graph G, another graph called the cycle graph of G and denoted by C(G) can be derived. The cycle graph C(G) of G has as its vertices the chordless cycles of G and two vertices in C(G) are adjacent if and only if the corresponding chordless cycles have at least one edge in common.

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34

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

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We first prove a ``non-embeddable extensions' theorem for polyhedral graph embeddings. Let G be a ``weakly 4-connected' planar graph. We describe a set of constructions that produce a finite list of non-planar graphs, each having a minor isomorphic to G, such that every non-planar weakly 4-connected graph H that has a minor isomorphic to G has a minor isomorphic to one of the graphs in the list. The theorem is more general and applies in particular to polyhedral embeddings in any surface. We discuss an approach to proving Jorgensen's conjecture, which states that if G is a 6-connected graph w

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35

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.

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Graphs are powerful data structure for representing objects and their relationships. They are extremely useful in the study of dynamical systems, evaluating how different agents interact among each other and behave. An example is represented by the consensus problem where a graph models a set of agents that locally interact and exchange their opinions with the aim of reaching a common opinion (consensus state). At the same time, many learning techniques rely on graphs exploiting their potentialities in modeling the relationships between data and determining additional features relate

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36

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

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37

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.

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38

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

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39

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.

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40

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.

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41

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.

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42

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.

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43

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

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Recursion is a fundamental tool of mathematics used to define, construct, and analyze mathematical objects. This work employs induction, sieving, inversion, and other recursive methods to solve a variety of problems in the areas of algebraic number theory, topological and combinatorial graph theory, and analytic probability and statistics. A common theme of recursively defined functions, weighted sums, and cross-referencing sequences arises in all three contexts, and supplemented by sieving methods, generating functions, asymptotics, and heuristic algorithms. In the area of number theory, this

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44

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

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Voltage graph theory can be used to describe embeddings of product graphs if one factor is a Cayley graph. We use voltage graphs to explore embeddings of various products where one factor is a hypercube, describing some minimal and symmetrical embeddings. We then define a graph product, the weak symmetric difference, and illustrate a voltage graph construction useful for obtaining an embedding of the weak symmetric difference of an arbitrary graph with a hypercube.

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45

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

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46

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.

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47

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

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We adopt a novel topological approach for graphs, in which edges are modelled as points as opposed to arcs. The model of classical <i>topologized graphs</i> translates graph isomorphism into topological homeomorphism, so that <i>all</i> combinatorial concepts are expressible in purely topological language. This allows us to extrapolate concepts from finite graphs to infinite graphs equipped with a compatible topology, which, dropping the classical requirement, need not be unique. We bring standard concepts from general topology to bear upon questions of a combinatorial inspiration,

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48

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

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Paul Gunther (1966), proved the following result: Given a continuous function f on a compact surface M of constant curvature -1 and its periodic lift g to the universal covering, the hyperbolic plane, then the averages of the lift g over increasing spheres converge to the average of the function f over the surface M. Heinz Huber (1956) considered the following problem on the hyperbolic plane H: Consider a strictly hyperbolic subgroup of automorphisms on H with compact quotient, and choose a conjugacy class in this group. Count the number of vertices inside an increasing ball, which are images

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49

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.

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Systems with topologically ordered ground states are considered to be promising candidates for quantum memories. These systems are characterised by a degenerate ground eigenspace separated by an energy gap from the rest of the spectrum. Consequently, topologically ordered systems are resilient to local noise since local errors are suppressed by the gap. Often, knowledge of the gap is not available and a direct approach to the problem is impractical. The first half of this thesis considers the problem of estimating the energy gap of a general class of Hamiltonians in the thermodynamical limit.

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50

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

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In graph theory, as in many fields of mathematics, one is often interested in finding the maxima or minima of certain functions and identifying the points of optimality. We consider a variety of functions on graphs and hypegraphs and determine the structures that optimize them. A central problem in extremal (hyper)graph theory is that of finding the maximum number of edges in a (hyper)graph that does not contain a specified forbidden substructure. Given an integer n, we consider hypergraphs on n vertices that do not contain a strong simplex, a structure closely related to and containing a simp

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