Star sets and related aspects of algebraic graph theory.

Topics in Algebraic Graph Theory (Encyclopedia of Mathematics and its Applications series) by Lowell W. Beineke. The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry).

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 opti-.

The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). Other books cover portions of this material, but none of these have such a wide scope.

This master thesis is a contribution to the area of algebraic graph theory and the study of some generalizations of regularity in bipartite graphs. In Chapter 1 we recall some basic concepts and results from graph theory and linear algebra. Chapter 2 presents some simple but relevant results on graph spectra concerning eigenvalue interlacing.

The goal of this thesis is to apply techniques from algebraic graph theory to finite incidence geometry. The incidence geometries under consideration include projective spaces, polar spaces and near polygons. These geometries give rise to one or more graphs.

A graph consists of a set of elements together with a binary relation defined on the set. Graphs can be represented by diagrams in which the elements are shown as points and the binary relation as lines joining pairs of points. It is this representation which gives graph theory its name and much of its appeal. However, the true importance of graphs is that, as basic.

This thesis introduces and studies the two-variable chromatic polynomial for signed graphs. In Chapter 2 we introduce the basic language used in graph theory. Chapter 3 begins with an introduction to signed graphs. The main results of this paper appear in Chapters 4 and 5. In Chapter 4, we.

Algebraic Graph Theory. Authors (view affiliations) Chris Godsil; Gordon Royle; Textbook. 2.6k Citations; 4 Mentions;. algebra Eigenvalue graph graph theory graphs homomorphism Laplace operator Matrix Matrix Theory Morphism polygon polynomial. Authors and affiliations. Chris Godsil. 1.

For PhD Thesis, see here. This page is about Senior thesis. This page is about Senior thesis. In order that senior thesis produced by Harvard math students are easier for other undergrads to benefit from, we would like to exhibit more senior theses online (while all theses are available through Harvard university archives, it would be more convenient to have them online).

Computer Science Theory, Algebraic Graph Theory, Combinatorics. The girth of a graph is the length of the shortest cycle in a graph, and the abelian girth of a graph is the girth of the graph's universal abelian covering graph.

Abstract. Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects.

View Algebraic Graph Theory Research Papers on Academia.edu for free.