Analysis of Eccentricity-Based Topological Invariants with Zero-Divisor Graphs

Abstract

Let R = Z ♭ 1 ♭ 2 ♭ 3 × Z q 2 be a commutative ring, where ♭ 1 , ♭ 2 , ♭ 3 are distinct primes, and q is any prime integer. A zero divisor graph J R of ring R is a graph with vertex set consist of zero divisors elements of R and any two vertices a , b are adjacent if and only if a b = 0 . A topological index is a numerical number associated with the graph and may be helpful to correlate the graph with certain of its physical/chemical properties. In this paper, we have computed some eccentricity based topological indices of J R , namely, atom-bond connectivity index ( AB C 5 ), eccentricity-based harmonic index of fourth type ( H 4 J ), geometric-arithmetic eccentricity index ( G A 4 J ), eccentricity-based third Zagreb index, and eccentricity-based first Zagreb index.