Some recurrence relations for the energy of cycle and path graphs

Abstract

Energy of a graph, first defined by E. Hiickel as the sum of absolute values of the eigenvalues of the adjacency matrix while searching for a method to obtain approximate solutions of Schrodinger equation for a class of organic molecules, is an important sub area of graph theory. This equation is a second order differential equation which include the energy of the corresponding system. The energy of many graph types are well-known in literature. To know the energy of a molecule is an important aspect in Chemical Graph Theory. Two classes, cycles and paths, show serious differences from others as the eigenvalues are trigonometric algebraic numbers which makes it difficult to calculate the energy of the corresponding graph. Here we obtain the polynomials and recurrence relations for the spectral polynomials of cycles and paths to find the energy of larger graphs easier than the classical way.