On Symmetric Neighbors degree sum exponent matrix

Abstract

Recently, exponent matrices have emerged as a dynamic tool for studying networks by measuring node centrality. In this work, we define a Symmetric Neighbors degree sum exponent matrix SN E(G) of a graph G whose (i, j)th entry is δδji + δδij for i ̸= j, it is zero otherwise, where δi is the Neighbors degree sum of a vertex vi in G. Inspired by the applications of Neighbors degree sum in redefining various degree based topological indices, we introduce characteristic polynomial of SN E(G), termed as Symmetric Neighbors degree sum exponent polynomial and the sum of absolute value of eigenvalue of SN E(G) matrix is called as Symmetric Neighbors degree sum exponentenergy. In this paper, we obtain the Neighbors degree sum exponent polynomial and Neighbors degree sum exponent energy of some graphs.