DEGREE SUM ENERGY OF NON-COMMUTING GRAPH FOR DIHEDRAL GROUPS

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Published: Sep 28, 2022
DOI: https://doi.org/10.22452/mjs.sp2022no.1.5
Keywords:
Non-commuting graph dihedral group degree sum matrix energy of graph

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Mamika Ujianita Romdhini
Universiti Putra Malaysia, MALAYSIA.
Athirah Nawawi
Universiti Putra Malaysia, MALAYSIA.

Abstract

For a finite group G, let Z(G) be the centre of G. Then the non-commuting graph on G, denoted by ΓG, has G\Z(G) as its vertex set with two distinct vertices vp and vq joined by an edge whenever vpvq ≠ vqvp. The degree sum matrix of a graph is a square matrix whose (p,q)-th entry is dvp + dvq whenever p is different from q, otherwise, it is zero, where dvi is the degree of the vertex vi. This study presents the general formula for the degree sum energy, EDS (ΓG), for the non-commuting graph of dihedral groups of order 2n, D2n, for all n ≥ 3.

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How to Cite
Mamika Ujianita Romdhini, & Nawawi, A. . (2022). DEGREE SUM ENERGY OF NON-COMMUTING GRAPH FOR DIHEDRAL GROUPS . Malaysian Journal of Science, 41(sp1), 34–39. https://doi.org/10.22452/mjs.sp2022no.1.5
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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