On spectral graph theory : a chemical application

Abstract

In recent years, Spectral 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 about the graph. There is still a contin uous development of the theory of graph spectra and this makes it one of the most important and relevant parts of algebraic graph theory. The surge in importance of the index of graphs in page ranking, wavelet theory, virus spreading and in many other fields where networks are important lead us to give a few of the hounds of the index together with some of its applications.