Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 38 for “"regular graphs"”.
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Distance-Regular Graphs and Generalizations
… (sigma) of (GAMMA). Distance-transitive graphs have certain combinatorial properties, which can be studied independently; a graph with these properties is called distance-regular.
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Matchings, Connectivity, and Eigenvalues in Regular Graphs
We study extremal and structural problems in regular graphs involving various parameters. In Chapter 2, we obtain the best lower bound for the matching number over $n$-vertex connected regular graphs in terms of edge-connectedness and determine when the matching number is minimized. We also …
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Chromatic Thresholds of Regular Graphs with Small Cliques
<p>The chromatic threshold of a class of graphs is the value <em>θ</em> such that any graph in this class with a minimum degree greater than <em>θn</em> has a bounded chromatic number. Several important results related to the chromatic threshold of triangle-free graphs have been reached in the last …
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Nested (2,r)-regular graphs and their network properties.
<p>A graph <i>G</i> is a (<i>t</i>, <i>r</i>)-regular graph if every collection of <i>t</i> independent vertices is collectively adjacent to exactly <i>r</i> vertices. If a graph <i>G</i> is (2, <i>r</i>)-regular where <i>p</i>, <i>s</i>, and <i>m</i> are positive integers, and <i>m</i> ≥ 2, then …
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Spectrum of some regular graphs with widely spaced modifications
… have high multiplicities. As the trees grow, the graphs of those eigenvalues approach a piecewise-constant "Cantor function", which is different from the corresponding properties of the infinite tree. The second part studies the effect of "widely spaced" modifications on the spectrum of some type …
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The Structure and Properties of Clique Graphs of Regular Graphs
… </em>(<em>G</em>) are analyzed for graphs <em>G </em>that are non-complete, regular with degree <em>δ </em>, and where every edge of <em>G </em>is contained in a <em>t </em>-clique. In a clique graph <em>cl</em><sub><em>t</em></sub><em> </em>(<em>G</em>), all cliques of order <em>t …
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A Characterization of Large (<em>t,r</em>)-Regular Graphs.
… graph <em>G</em> is a (<em>t</em>,<em>r</em>)-regular graph if every collection of <em>t</em> independent vertices is collectively adjacent to exactly <em>r</em> vertices. In this thesis, we will present a complete characterization of (<em>t</em>,<em>r</em>)-regular graphs of order <em>n</em> …
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Interplay between FQH Ground States, Regular Graphs, Binary Invariants, and [formula] -Algebras
… ground state is essentially a superposition of regular graphs. In this paradigm, algebro-analytic properties of polynomial wavefunctions are synonymous with graph-theoretic properties. (2) We introduce a new possible local property of ground states called separability. Utilizing separability, a …
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Algebraic methods in graph theory
… in understanding the structural properties of graphs. In general, we can use the eigenvalues of the adjacency matrix of a graph to study various properties of graphs. In this thesis, we obtain the whole spectrum of a family of graphs called Wenger graphs Wm (q ). We also study the a conjecture …
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Applications of Schur rings in algebraic combinatorics: graphs, partial difference sets and cyclotomic schemes
… considered: (1) characterization of commuting graphs, (2) consideration of strongly regular graphs and partial difference sets and (3) investigation of cyclotomic schemes. The first part deals with graphs with commuting adjacency matrices. Here, we give results for commuting regular graphs and …
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An investigation of relationships between graph theory and coding theory
… and combinatorial properties of completely regular codes in distance-regular graphs. One of the main tools is the generalisation of Lloyd's Theorem.<br/><br/>There are connections with designs, orthogonal latin squares and finite projective planes and various existence and non-existence …
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Spectral analysis in bipartite biregular graphs and community detection
This thesis concerns to spectral gap of random regular graphs and consists of two main con- tributions. First, we prove that almost all bipartite biregular graphs are almost Ramanujan by providing a tight upper bound for the non trivial eigenvalues of its adjacency operator, proving Alon's …
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Graph Isomorphism Algorithms Based on Trees and Paths.
… for testing isomorphism of two classes of graphs: the strongly regular graphs, which have been difficult for many previous isomorphism algorithms to process, and the compact graphs (graphs with diameter of 2 whose complements also have diameter of 2).The strongly regular graphs algorithm is …
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Subconstituent Algebras of Latin Squares
… scheme. One also may construct several strongly regular graphs on the positions of a Latin square, where adjacency corresponds to any subset of the nonidentity relations described above. We describe the local spectrum and subconstituent algebras of such strongly regular graphs. Finally, we study …
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Bounds on k-Regular Ramanujan Graphs and Separator Theorems
Expander graphs are a family of graphs that are highly connected. Finding explicit examples of expander graphs which are also sparse is a difficult problem. The best type of expander graph in a. certain sense is a Ramanujan graph. Families of graphs that have separator theorems fail to be Ramanujan …
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Ultraconnected and Critical Graphs
… investigate the ultraconnectivity condition on graphs, and provide further connections between critical and ultraconnected graphs in the positive definite partial matrix completion problem. We completely characterize when the join of graphs is ultraconnected, and prove that ultraconnectivity is …
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Distances in planar graphs
… of the face. A plane graph is ρ-face-degree regular if every face has face-degree ρ. This thesis begins with a literature review outlining the results and methods of papers studying planar graphs, particularly those solving the degree diameter problem for various kinds of ρ-facedegree regular …
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Polynomials of the Adjacency Matrix of a Graph (distance-Transitive, Distance-Regular, Orbit)
Given graphs (GAMMA) and (DELTA), and a real polynomial r(x), we will say that (DELTA) is generated from (GAMMA) by r(x) if r(A((GAMMA))) = A((DELTA)) where A((GAMMA)) and A((DELTA)) are adjacency matrices. For several interesting classes of graphs it is possible to determine all of the graphs …
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