ON SYMMETRIC NEIGHBORS DEGREE SUM EXPONENT MATRIX

Year 2026, Volume: 16 Issue: 4 , 536 - 542 , 07.04.2026

Pushpa Nalwad Narayan Swamy , Aditya Biradar

https://izlik.org/JA24AP99JL

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 $S_{N}E(G)$ of a graph $G$ whose $(i,j)^{th}$ entry is $\delta_i^{\delta_j}+\delta_j^{\delta_i}$ for $i\neq j$, it is zero otherwise, where $\delta_i$ is the Neighbors degree sum of a vertex $v_i$ in $G$. Inspired by the applications of Neighbors degree sum in redefining various degree based topological indices, we introduce characteristic polynomial of $S_{N}E(G)$, termed as Symmetric Neighbors degree sum exponent polynomial and the sum of absolute value of eigenvalue of $S_{N}E(G)$ 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

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