Topological indices of the zero-divisor graph for the direct product of finite commutative rings

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran.

Abstract

A topological index is a numerical quantity associated with the topological structure of a graph, used to describe certain of its properties. In this paper, we compute several degree-based topological indices of the zero-divisor graph $\Gamma(R)$ when $R$ is the commutative ring $\mathbb{Z}_p \times \mathbb{Z}_{p^2}$ and $\mathbb{Z}_p \times \mathbb{Z}_{2p}$ for a prime $p>2$. For the commutative ring $R$ with the set of zero-divisors $Z(R)$, the simple graph $\Gamma(R)$ contains the vertex set $V\left(\Gamma(R)\right)=Z(R)\setminus \{0\}$ and the edge set $E\left(\Gamma(R)\right)=\{uv | u, v \in Z(R)\setminus \{0\}~\&~uv=vu=0\}$.

Keywords

References

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Algebraic Structures and Their Applications

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Available Online from 21 July 2026

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