ON SYMMETRIC NEIGHBORS DEGREE SUM EXPONENT MATRIX

ON SYMMETRIC NEIGHBORS DEGREE SUM EXPONENT MATRIX

Pushra Nalwand, Narayan Swamy, Aditya Biradar

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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 SNE(G) of a graph G whose (i, j)th entry is δ δj i + δδi j 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 SNE(G), termed as Symmetric Neighbors degree sum exponent polynomial and the sum of absolute value of eigenvalue of SNE(G) matrix is called as Symmetric Neighbors degree sum exponent energy. In this paper, we obtain the Neighbors degree sum exponent polynomial and Neighbors degree sum exponent energy of some graphs.

Keywords

Graphs, Neighbors degree sum, Symmetric Neighbors degree sum exponent matrix, Symmetric Neighbors degree sum exponent polynomial and energy.