DEGREE EXPONENT SUM ENERGY OF COMMUTING GRAPH FOR DIHEDRAL GROUPS

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Published: Sep 28, 2022
DOI: https://doi.org/10.22452/mjs.sp2022no1.6
Keywords:
Commuting graph dihedral group degree exponent sum matrix energy of graph

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Mamika Ujianita Romdhini
Universiti Putra Malaysia, MALAYSIA.
Athirah Nawawi
Universiti Putra Malaysia, MALAYSIA.
Chen Chuei Yee
Universiti Putra Malaysia, MALAYSIA.

Abstract

For a finite group G and a nonempty subset X of G, we construct a graph with a set of vertex X such that any pair of distinct vertices of X are adjacent if they are commuting elements in G. This graph is known as the commuting graph of G on X, denoted by ΓG [X]. The degree exponent sum (DES) matrix of a graph is a square matrix whose (p,q)-th entry is is   dvp dvq + dvqdvp whenever p is different from q, otherwise, it is zero, where dvp (or dvq ) is the degree of the vertex vp (or vertex, vq) of a graph. This study presents results for the DES energy of commuting graph for dihedral groups of order 2n, using the absolute eigenvalues of its DES matrix.

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How to Cite
Mamika Ujianita Romdhini, Nawawi, A. ., & Chen Chuei Yee. (2022). DEGREE EXPONENT SUM ENERGY OF COMMUTING GRAPH FOR DIHEDRAL GROUPS . Malaysian Journal of Science, 41(sp1), 40–46. https://doi.org/10.22452/mjs.sp2022no1.6
Issue
Vol. 41 No. sp1 (2022): Special Issue Virtual Symposium On Multidisciplinary Science 2021 (V-SMS2021)
Section
V-SMS2021

Licensee MJS, Universiti Malaya, Malaysia. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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