Abstract
This article is devoted to the determination of edge-based eccentric topological indices of a zero divisor graph of some algebraic structures. In particular, we computed the first Zagreb eccentricity index, third Zagreb eccentricity index, geometric-arithmetic eccentricity index, atom-bond connectivity eccentricity index and a fourth type of eccentric harmonic index for zero divisor graphs associated with a class of finite commutative rings.
Highlights
Algebraic structures have been studied for their close affiliation with representation theory and number theory, and they have been extensively studied in combinatorics [1,2]
This section is devoted on the discussion of eccentric topological indices based on the edges of zero divisor graphs for rings Za × Zb with a = p1 p2, p2 and b = q2, where p1, p2, p and q are prime numbers
This article emphasizes the computation of first Zagreb eccentricity index, third Zagreb eccentricity index, geometric-arithmetic eccentricity index, atom-bond connectivity eccentricity index and the fourth type of eccentric harmonic index for zero divisor graphs associated with algebraic structures that are commutative rings Z p1 p2 × Zq2 and Z p2 × Zq2
Summary
Algebraic structures have been studied for their close affiliation with representation theory and number theory, and they have been extensively studied in combinatorics [1,2]. A foundational role of molecular descriptors is to consider molecules as real bodies and transform them into numbers, which enables mathematics to play a key role in chemistry, pharmaceutical sciences, environmental protection, quality control and health research. These molecular descriptors are graph invariants and are usually known as topological indices. By using topological indices we correlate various characteristics of a chemical structure in order to characterize it. These days there is an area of research devoted to computing topological indices for various structures
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