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.

On distance dependent entropy measures of poly propylene imine and zinc porphyrin dendrimers

“…By adopting this strategy, several researchers studied different objects such as algebraic objects [1], physio‐chemical properties of chemical structures [2–5] drugs used for anti cancer treatment [6–8], BC‐subtrees [9] and interconnection networks [10–12]. Due to vast applications, the study TIs of different types such as degree based [13, 14], distance and eccentricity based indices [15–17] and indices for graph operations [18] is among the modern research trends in the area of graph theory. Recently, Ghorbani et.…”

Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤ ℊ Liu1, Rauf2, Aslam3 et al. 2022Journal of Function SpacesSelf Cite1000View full textAdd to dashboardCite

“…Some well-known distance-based topological indices are the Wiener index, Hosoya index, and Estrada index [20,21]. For details related to the computation of Hosoya and Harary polynomial of zero divisor graphs associated to some commutative rings, the readers can see [22][23][24].…”

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

“…This article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. This investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process:…”