Formulae and recurrence relations on spectral polynomials of some graphs

Abstract

Energy of a graph, firstly defined by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix while searching for a method to obtain approximate solutions of Schrödinger equation for a class of organic molecules, is an important sub area of graph theory. Schrodinger equation is a second order differantial equation which include the energy of the corresponding system. Here we obtain the polynomials and recurrence relations for the spectral (characteristic) polynomials of some graphs.