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All Journal 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)
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

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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 $n$.
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 Shofiyulloh, M. Yogi Anggara Zuha, Jaqueline Widad