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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan
Bawana, Agista Surya
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Some Topological Indices of Order Divisor Graphs of Cyclic Groups Bawana, Agista Surya; Susanti, Yeni
Journal of the Indonesian Mathematical Society Vol. 31 No. 1 (2025): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i1.1717

Abstract

This study investigates order divisor graphs' structural and topological properties derived from cyclic groups. Focusing on the relationship between group order and graph topology, we explore key indices, including the Wiener index, the Harary index, the first Zagreb index, and the second Zagreb index. We use a case-based approach to analyze graphs for cyclic groups of varying orders, from prime powers to more general composite structures. This work extends the theoretical framework of order divisor graphs and provides explicit formulations for their topological indices, highlighting the interplay between algebraic and graph-theoretic properties. These findings contribute to the broader understanding of algebraic graph theory and its applications.
ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP Bawana, Agista Surya; Sutjijana, Aluysius; Susanti, Yeni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 3 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss3pp1695-1702

Abstract

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., 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 if , for some and if . Moreover, we prove that if is even, then the independence number of is , where is the greatest odd divisor of and if is odd, then the independence number of is . Furthermore, the Wiener index of coprime graph of dihedral group has been stated here.
Some Properties of Cartesian Product of Non-Coprime Graph Associated with Finite Group Bawana, Agista Surya; Qonita, Niswah; Syarifudin, Abdul Gazir; Susanti, Yeni
Journal of the Indonesian Mathematical Society Vol. 31 No. 4 (2025): DECEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i4.2095

Abstract

This paper investigates several properties of the Cartesian product of two non-coprime graphs associated with finite groups. Specifically, we focus on key numerical invariants, namely the domination number, independence number, and diameter. The non-coprime graph associated with finite group $G$ is constructed with the vertex set $G\setminus \{e\}$ and connects two distinct vertices if and only if their orders are not coprime. Using this construction, we investigate the Cartesian products of non-coprime graphs associated with various types of groups, including nilpotent groups, dihedral groups, and $p$-groups. We derive several new results, including exact expressions for the domination number, independence number, and diameter of these Cartesian products.
Co-Authors Abdul Gazir Syarifudin Qonita, Niswah Sutjijana, Aluysius Yeni Susanti