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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Dimas Indrawadi
University of Mataram
Mathematics

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Fisrt Zagreb, Gutman, and Wiener Index of The Non-Coprime Graph for Dihedral Group Dimas Indrawadi; I Gede Adhitya Wisnu Wardhana; Hazzirah Izzati Hassim; Fariz Maulana
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/sqqdm542

Abstract

This study investigates the structure of non-coprime graphs derived from the dihedral groups of prime power order using approaches from graph theory and group theory. In molecular representation and pure mathematics, graphs serve a tool to illustrate the internal structure of systems through topological indices. A non-coprime graph is a graph formed by connecting two distinct vertices if the greatest common divisor (GCD) of their orders is not equal to one, meaning the two elements are not coprime. The primary focus of this research is to derive general formulas for the first Zagreb index, the Gutman index, and the Wiener index of non-coprime graphs constructed from the dihedral group ​. For the first Zagreb index, the cases and are considered, where is a prime number and is a positive integer. Meanwhile, for the Gutman and Wiener indices, the study focuses on the case, with as a positive integer. This research produces explicit formulas for the first Zagreb index, Gutman index, and Wiener index of the corresponding non-coprime graphs.
Co-Authors Fariz Maulana Hazzirah Izzati Hassim I Gede Adhitya Wisnu Wardhana