Degree kth power sum polynomial of generalized graphs related to the cycle

Abstract

The purpose of this paper is to introduce the concept of degree k^th power sum matrix of a graph G. There are some flaws in the definitions of generalized graphs related to the cycle and we correct these definitions. We compute degree k^th power sum polynomials of generalized graphs related to cycle. We establish the bounds for the largest degree k^th power sum eigenvalue and degree k^th power sum energy of graphs.