The spectrum of the adjacency matrix of graphs and regular subgraphs

Abstract

In recent years, graph theory has been recognised as an important indispensable mathematical tool in a wide variety of subjects ranging from operational research and chemistry to bioinformatics and linguistics. At the same time it has also emerged as a valuable mathematical discipline in its own right. A graph is not uniquely determined by its spectrum, however the spectrum of a graph contains some important information of a graph. A continuous development of the theory of graph spectra that has been taking place for more than forty years, and is still subject to constant development, led it to the present state of being one of the most important and relevant parts of algebraic graph theory.