Computing new degree-based topological indices associated with the zero-divisor graphs of finite commutative rings

Consider a commutative ring ℜ. Let ℨ*(ℜ) denote the set of zero-divisors of ℜ\{0}. A zero-division graph, denoted by Γ(ℜ), is a graph interrelated with the ring ℜ, where the vertex set consists of the elements in ℨ*(ℜ). In this graph, two vertices w1 and w2 are adjacent if and only if their product satisfies w1 w2 = w2 w1 = 0. In a recent research paper, we explore various degree-based topological indices related to Γ(R). Specifically, we investigate the graph structures for the types of commutative rings including ℤζ2, ℤζ3, ℤζ × ℤζ × ℤζ, ℤζ1 ζ2 and ℤζ2 1 × ℤζ2 where ζ, ζ1 and ζ2 are the primes. This study sheds light on the algebraic properties of these rings and provides insights into their underlying graph structures.