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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Jurnal Sains Dasar Jurnal Fourier BAREKENG: Jurnal Ilmu Matematika dan Terapan Jambura Journal of Mathematics Jurnal Matematika UNAND Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Jurnal Ilmiah Matematika Jurnal Diferensial Journal of Fundamental Mathematics and Applications (JFMA) International Journal of Computing Science and Applied Mathematics-IJCSAM
Arif Munandar
UIN Sunan Kalijaga Yogyakarta
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Public Health Transportation

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Connectivity Indices of Power Graphs over Dihedral Groups of a Certain Order Munandar, Arif
Jurnal Sains Dasar Vol. 14 No. 1 (2025): April 2025
Publisher : Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

The dihedral group is a mathematical structure generated by rotational and reflection symmetries. In this study, the representation of the group is described using a power graph, where all elements of the group are treated as vertices, and two distinct elements are considered adjacent when one is a power of the other. By analyzing the structural patterns of the resulting power graphs, various connectivity indices can be determined, particularly for dihedral groups whose orders are powers of a prime number. This research focuses on six specific connectivity indices: the first Zagreb index, the second Zagreb index, the Wiener index, the hyper-Wiener index, the Harary index, and the Szeged index.
New Entropy Pythagorean Fuzzy Set And Its Application In Multicriteria Decision Making Munandar, Arif
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.439-450.2025

Abstract

In this study, a new entropy measure for Pythagorean fuzzy sets is proposed. The validity of the entropy is rigorously verified through the satisfaction of keyaxiomatic properties such as minimality, maximality, symmetry, and resolution. Oncevalidated, the newly developed entropy is applied to a multi-criteria decision-making(MCDM) problem using the TOPSIS method. The integration of this entropy with TOPSIS provides a robust and systematic approach to determining optimal alternatives indecision-making scenarios involving uncertainty and imprecision. The proposed methodenhances the ability to model and analyze complex problems, thereby contributing a noveland effective tool to the field of fuzzy decision-making
Dimensi Metrik Lokal pada Operasi Korona Graf Ular Segitiga dengan Graf Lintasan Orde Dua Zuha, Jaqueline Widad; Rahmadi, Deddy; Munandar, Arif
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.27365

Abstract

Graphs were first introduced by Leonard Euler through the Königsberg Bridge problem in 1736. Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. The concept of distance in graphs leads to the notions of metric dimension and local metric dimension. Let $W \subset V(G)$ with $W = \{w_1, w_2, \dots, w_n\}$. The representation of a vertex $x \in V(G)$ with respect to $W$ is defined by $r(x \mid W) = (d(x, w_1), d(x, w_2), \dots, d(x, w_n)).$ The set $W$ is called a local resolving set of $G$ if for every pair of adjacent vertices $u, v \in V(G)$, $r(u \mid W) \ne r(v \mid W)$. The minimum cardinality of such a set is called the local metric dimension of $G$ and is denoted by $\dim_{\ell}(G)$. This research aims to determine the metric dimension and local metric dimension of the triangular snake graph $T_n$, as well as graphs obtained from the corona operation between $T_n$ and a path graph of order two. The method used is a literature study with an analysis of graph structure and vertex distances. The results show that both the metric dimension and the local metric dimension of the triangular snake graph are equal to $2$. Moreover, the local metric dimension of $T_n \odot P_2$ is $2n+1$, while that of $P_2 \odot T_n$ is $n+3$ for odd $n$ and $n+2$ for even $n$.
Prime Graph Over Semidihedral Group and Its Connectivity Indices Riyanto Riyanto; Arif Munandar
Jurnal Fourier Vol. 15 No. 1 (2026)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2026.151.54-62

Abstract

This study investigates the structural properties and topological connectivity indices of the prime graph associated with the semidihedral group of order 2 raised to the power of n, whose vertex set consists of all elements of the group. Two distinct vertices are adjacent precisely when the greatest common divisor of their orders is a prime number. Since the identity element has order one, it is not adjacent to any other vertex and therefore forms an isolated vertex. Consequently, the prime graph is disconnected and consists of the isolated identity element together with a non-trivial connected component containing all remaining group elements. The vertex set is partitioned into three disjoint subsets consisting of the identity element, elements of order two, and elements of order greater than two. Based on this partition, we characterize the degree sequence, diameter, radius, and clique number of the graph. Furthermore, exact closed-form analytical formulas are obtained for several fundamental degree-based and distance-based topological connectivity indices, including the First Zagreb index, Wiener index, Hyper-Wiener index, Harary index, and Forgotten index.
Connectivity of Power Graphs of Cyclic Groups with Specific Orders Riyanto; Arif Munandar
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 12 No. 2 (2026)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v12i2.9603

Abstract

The power graph is defined as a graph whose vertexset consists of the elements of a group, where two vertices arejoined by an edge if one element is a power of the other. In thisresearch we discuss the power graph of a cyclic group of order n=pq, with p and q distinct prime numbers, illustrates theconnectivity among its vertices and reveals important topologicalproperties such as the diameter and the clique number. Fur-thermore, this study also examines the degrees of the verticesand provides an analysis of the Hamiltonian, Eulerian, andplanar characteristics of the graph. These findings highlighthow algebraic structures can be effectively explored throughgraph-theoretical perspectives, offering deeper insights into theinterplay between group theory and graph topology.
Connectivity of Non-Coprime Graph over Dihedral Group Winda Cahya Dwi Wahyuni; Arif Munandar
Jurnal Matematika, Statistika dan Komputasi Vol. 23 No. 1 (2026): September 2026
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/y76mg453

Abstract

Let Γ be the non-coprime graph of the dihedral group of order 2n. This research investigates the connectivity properties of Γ, particularly its Eulerian, semi-Eulerian, Hamiltonian, and planar properties. The research begins by examining several properties related to the dihedral group, and then identifying the connectivity patterns that are formed in the non-coprime graph through the analysis of the order of elements in the group. These patterns then serve as the basis for determining its connectivity properties. The results show that Γ is Eulerian when n = 2k, where k ≥ 2, and semi-Eulerian if and only if n = 2p, where p is an odd prime. Furthermore, the graph is Hamiltonian for n = 2k or n = 2p, where p is an odd prime. In addition, the graph is planar if and only if n = 2 or n = 3. These results indicate that the factorization form of n strongly influences the connectivity structure and graph properties of the non-coprime graph over the dihedral group.
Co-Authors Carlinda, Ardha Febrianti, Alfina Berliana Ilma Nindita Ramadhani Indah Emilia Wijayanti Khurul Wardati Muhammad Lutfi Prakasta Nuur, Imam Hafiidz Rahmadi, Deddy Rahmadina, Alifah Fitria Riyanto Riyanto Riyanto Shofiyulloh, M. Winda Cahya Dwi Wahyuni Yogi Anggara Zuha, Jaqueline Widad