EDGE-adjacency in graphs

Abstract

Energy of a graph was defined by E. Huckel as the sum of absolute values of the eigenvalues of the adjacency matrix during his search to find a method to obtain approximate solutions of Schrodinger equation for a class of organic molecules. It is an important sub-area of graph theory called spectral graph theory. Schrodinger equation is a second order differential equation which includes the energy of the corresponding system and as we can model all molecules with graphs, we can calculate the energy of a given graph. Here we obtain the exact formulae and recurrence relations for the edge-characteristic and incidency polynomials of some well-known graph classes.