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All Journal Journal of the Indonesian Mathematical Society Journal of Fundamental Mathematics and Applications (JFMA)
Semil @ Ismail, Ghazali
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Decision Sciences, Operations Research & Management Mathematics

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THE CHEMICAL TOPOLOGICAL GRAPH ASSOCIATED WITH THE NILPOTENT GRAPH OF A MODULO RING OF PRIME POWER ORDER Malik, Deny Putra; Husni, Muhammad Naoval; Miftahurrahman, Miftahurrahman; Wardhana, I Gede Adhitya Wisnu; Semil @ Ismail, Ghazali
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.20269

Abstract

Chemical topological graph theory constitutes a subdomain within mathematical chemistry that leverages graph theory to model chemical molecules.  In this context, a chemical graph serves as a graphical representation of molecular structures. Specifically, a chemical molecule is portrayed as a graph wherein atoms are denoted as vertices, and the interatomic bonds are represented as edges within the graph. Various molecular properties are intricately linked to the topological indices of these molecular graphs. Notably, commonly employed indices encompass the Wiener Index, the Gutman Index, and the Zagreb Index.  This study is directed towards elucidating the numerical invariance and topological indices inherent to a nilpotent graph originating from a modulo integer ring with prime order. Consequently, the investigation seeks to discern how the Wiener Index, the Zagreb Index, and other characteristics of the nilpotent graph manifest within a ring of integers modulo prime order powers.
Forgotten Topological Index of The Zero Divisor Graph for Some Rings of Integers Semil @ Ismail, Ghazali; Sarmin, Nor Haniza; Alimon, Nur Idayu; Maulana, Fariz
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.v31i1.1827

Abstract

A topological index is a numerical value that provides information about the structure of a graph. Among various degree-based topological indices, the forgotten topological index (F-index) is of particular interest in this study. The F-index is calculated for the zero divisor graph of a ring R. In graph theory, the zero divisor graph of R is defined as a graph with vertex set the zero-divisors of R, and for distinct vertices a and b are adjacent if a · b = 0. This research focuses on the zero divisor graph of the commutative ring of integers modulo 2ρn where ρ is an odd prime and n is a positive integer. The objectives are to determine the set of all zero divisors, analyze the vertex degrees of the graph, and then compute the F-index of the zero divisor graph. Using algebraic techniques, we derive the degree of each vertex, the distribution of vertex degrees, and the number of edges in the graph. The general expression for the F-index of the zero divisor graph for the ring is established. The results contribute to understanding topological indices for algebraic structures, with potential applications in chemical graph theory and related disciplines.
Co-Authors Alimon, Nur Idayu Husni, Muhammad Naoval I Gede Adhitya Wisnu Wardhana Malik, Deny Putra Maulana, Fariz Miftahurrahman, Miftahurrahman Sarmin, Nor Haniza