https://doi.org/10.30598/barekengvol17iss3pp1695-1702
September 2023 Volume 17 Issue 3 Page 1695–1702
P-ISSN: 1978-7227 E-ISSN: 2615-3017
BAREKENG: Journal of Mathematics and Its Applications
1695
ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF
COPRIME GRAPH OF DIHEDRAL GROUP
Agista Surya Bawana
1*
, Aluysius Sutjijana
2
, Yeni Susanti
3
1,2,3
Department of Mathematics, Faculty of Mathematics and Natural Science, Gadjah Mada University
Sleman, D.I. Yogyakarta, 55281, Indonesia
Corresponding author’s e-mail: * agista.surya.bawana@mail.ugm.ac.id
ABSTRACT
Article History:
The coprime graph of a finite group , denoted by
, is a graph with vertex set such that two
distinct vertices and are adjacent if and only if their orders are coprime, i.e., gcd(||, ||) =
1 where |x| is the order of x. In this paper, we complete the form of the coprime graph of a
dihedral group that was given by previous research and it has been proved that ℎ(
2
)=
∞ if = 2
, for some ≥2 and ℎ(
2
)=3 if ≠2
. Moreover, we prove that if is
even, then the independence number of
2
is (
2
) = 2 − , where is the greatest odd
divisor of and if is odd, then the independence number of
2
is (
2
)= . Furthermore,
the Wiener index of coprime graph of dihedral group has been stated here.
Received: 12
th
May 2023
Revised: 13
th
August 2023
Accepted: 22
nd
August 2023
Keywords:
Dihedral groups;
Coprime graph;
Girth;
Independence number;
Wiener index.
This article is an open access article distributed under the terms and conditions of the
Creative Commons Attribution-ShareAlike 4.0 International License.
How to cite this article:
A. S. Bawana, A. Sutjijana and Y. Susanti., “ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF
DIHEDRAL GROUP,” BAREKENG: J. Math. & App., vol. 17, iss. 3, pp. 1695-1702, September, 2023.
Copyright © 2023 Author(s)
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Research Article ∙ Open Access