This volume provides an up-to-date survey of current research activity in several areas of combinatorics and its applications. These include distance-regular graphs, combinatorial designs, coding theory, spectra of graphs, and randomness and computation. The articles give an overview of combinatorics that will be extremely useful to both mathematicians and computer scientists.

Line graphs have the property that their least eigenvalue is greater than, or equal to, -2, a property shared by generalized line graphs and a finite number of so-called exceptional graphs. This book deals with all these families of graphs in the context of their spectral properties. Technical descriptions of these graphs are included in the appendices, while the bibliography provides over 250 references. It will be an important resource for all researchers with an interest in algebraic graph theory.

Graph theory is an important branch of contemporary combinatorial mathematics. By describing recent results in algebraic graph theory and demonstrating how linear algebra can be used to tackle graph-theoretical problems, the authors provide new techniques for specialists in graph theory. The book explains how the spectral theory of finite graphs can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labeling of graph vertices,...

A self-contained introduction to the theory of graph spectra including exercises and an extensive bibliography.

A self-contained introduction to the theory of graph spectra including exercises and an extensive bibliography.