Neighbors degree sum exponent polynomial and neighbors degree sum exponent energy of graphs

Abstract

Recently exponent matrix have come out to be working as dynamic tool to study networks by measuring the centrality node. In this work, we define a Neighbors degree sum exponent matrix NE(G) of a graph G whose (i,j)-th entry is d_i for i not equal to j, it is zero otherwise, where d_i is the Neighbors degree sum of a vertex v_i in G. Inspired from the applications of Neighbor degree sum in redefining various degree based topological indices, we introduce  characteristic polynomial of NE(G) to be known as Neighbors degree sum exponent polynomial and the sum of absolute value of eigenvalue of NE(G) matrix is called as Neighbors degree sum energy. In this paper, we obtain  the Neighbors degree sum exponent polynomial and  Neighbors degree sum exponent energy of some graphs.