Coefficients of Randic and Sombor characteristic polynomials of some graph types

Abstract

Let GG be a graph. The energy of GG is defined as the summation of absolute values of the eigenvalues of the adjacency matrix of GG. It is possible to study several types of graph energy originating from defining various adjacency matrices defined by correspondingly different types of graph invariants. The first step is computing the characteristic polynomial of the defined adjacency matrix of GG for obtaining the corresponding energy of GG. In this paper, formulae for the coefficients of the characteristic polynomials of both the Randic and the Sombor adjacency matrices of path graph PnPn , cycle graph CnCn are presented. Moreover, we obtain the five coefficients of the characteristic polynomials of both Randic and Sombor adjacency matrices of a special type of 3?regular graph RnRn.