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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) EIGEN MATHEMATICS JOURNAL
Suwastika, Erma
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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ON PROPERTIES OF PRIME IDEAL GRAPHS OF COMMUTATIVE RINGS Kurnia, Rian; Abrar, Ahmad Muchlas; Syarifudin, Abdul Gazir; Wijaya, Verrel Rievaldo; Supu, Nur Ain; Suwastika, Erma
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/barekengvol17iss3pp1463-1472

Abstract

The prime ideal graph of in a finite commutative ring with unity, denoted by , is a graph with elements of as its vertices and two elements in are adjacent if their product is in . In this paper, we explore some interesting properties of . We determined some properties of such as radius, diameter, degree of vertex, girth, clique number, chromatic number, independence number, and domination number. In addition to these properties, we study dimensions of prime ideal graphs, including metric dimension, local metric dimension, and partition dimension; furthermore, we examined topological indices such as atom bond connectivity index, Balaban index, Szeged index, and edge-Szeged index.
Topological Indices of the Relative Coprime Graph of the Dihedral Group Syarifudin, Abdul Gazir; Santi, Laila Maya; Faradiyah, Andi Rafiqa; Wijaya, Verrel Rievaldo; Suwastika, Erma
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14913

Abstract

Assuming that G is a finite group and H is a subgroup of G, the graph known as the relative coprime graph of G with respect to H (denoted as Γ_(G,H)) has vertices corresponding to elements of G. Two distinct vertices x and y are adjacent by an edge if and only if (|x|,|y|)=1 and x or y belongs to H. This paper will focus on  finding the general formula for some topological indices of the relative coprime graph of a dihedral group. The study of topological indices in graph theory offers valuable insights into the structural properties of graphs. This study is conducted by reviewing many past literatures and then from there we infer a new result. The obtained outcomes will include measurements of distance, degree of vertex, and various topological indices such as the first Zagreb index, second Zagreb index, Wiener index, and Harary index that are associated with distance and degree of vertex.
Topological Indices of Relative g-noncommuting Graph of Dihedral Groups Supu, Nur Ain; Muchtadi-Alamsyah, Intan; Suwastika, Erma
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 3 (NOVEMBER 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.3.1594.271-288

Abstract

Let G be a finite group, H be a subgroup of G and g be a fixed element of G. The relative g-noncommuting graph Γ(g,H,G) of G is defined as a graph with vertex set is G and two distinct vertices x and y are adjacent if [x, y] ̸= g or [x, y] ̸= g−1, where at least x or y belong to H. In this paper, we will discuss the relative g-non-commuting graph of the dihedral groups D(2n), in particular case when n is an odd number. We give several topological indices of the relative g-noncommuting graph of the dihedral groups D2n including the first Zagreb index, Wiener index, Edge-Wiener index, Hyper-Wiener index, and Harary index.
A Novel Approach to Topological Indices of the Power Graph Associated with the Dihedral Group of a Certain Order Syarifudin, Abdul Gazir; Santi, Laila Maya; Shaumi, Nurina Fadlila; Suwastika, Erma; Wardhana, I Gede Adhitya Wisnu
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.253

Abstract

Power graph of a group G, represented by \Gamma_G, is a graph where the vertex set consists of the elements of G. Two distinct vertices a, b \in G are connected by an edge if and only if there exists a positive integer m such that a^m = b or b^m = a. This study explores the utilization of a new approach to compute the topological indices of power graph associated with dihedral group with n=p^k, p is primes and k \in \mathbb{Z}. Results obtained indicate that the topological indices calculated using new approach yield the same values as those obtained with the conventional approach.
Co-Authors Abrar, Ahmad Muchlas Faradiyah, Andi Rafiqa I Gede Adhitya Wisnu Wardhana Intan Muchtadi Alamsyah Rian Kurnia, Rian Santi, Laila Maya Shaumi, Nurina Fadlila Supu, Nur Ain Wijaya, Verrel Rievaldo