Page 23 - programme book

AA-003
Neighbors Degree Sum Energy of Commuting and Non-Commuting Graph
for Dihedral Groups

Mamika Ujianita Romdhini 1,3,b) , Athirah Nawawi 1,2,a) , and Chuei Yee Chen 1,c)

1 Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang,
Selangor, Malaysia.
Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.
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3 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, 83125,
Indonesia.

a) Corresponding author: athirah@upm.edu.my
b) mamika@unram.ac.id
c) cychen@upm.edu.my

Abstract. Suppose that is a finite group and ( ) is the center of . In this paper, we discuss the
graph where the vertices set is \ ( ). The non-commuting graph of a group , denoted by , is

constructed by joining two distinct vertices , ∈ \ ( ) with an edge whenever ≠ .

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The complement of is the commuting graph of a group , , with two distinct vertices , ∈

\ ( ) are adjacent whenever = . The number of vertices adjacent to is defined as ,

which is the degree of Neighbors degree sum ( ) matrix of a graph is defined as a square matrix

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whose ( , )-th entry is + if and are adjacent, − if = or otherwise, it is zero.

This study presents the formulas of neighbors degree sum (NDS) energies of commuting and non-
commuting graphs for dihedral groups of order 2 , , for two cases−odd and even .
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Keywords: Energy of graph, Neighbors Degree Sum Matrix, Commuting graph, non-commuting
graph, Dihedral group.

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