On the Trinajstic index of zero divisor graphs

Abstract

In this paper, the Trinajstic index, a novel topological index, is analyzed within the framework of basic concepts in Graph Theory, particularly focusing on Zero-Divisor Graphs, excluding trees. The Trinajstic index, initially developed in the context of Chemical Graph Theory, investigates chemical structures based on a distance-balance concept. After constructing a pseudocode to calculate the Trinajstic index, the relevant algorithms were implemented using MATLAB. Subsequently, MATLAB codes for generating graphs and calculating the Trinajstic index were combined to compute the index for various graphs. Formulas relating to prime-based Zero-Divisor Graphs were derived and proven.