Wiener index of the Cozero-divisor graph of a finite commutative ring

2022/10/04 by Barkha Baloda, Praveen Mathil, Baloda, Barkha +5
Mathematics · #05C25 #05C50 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2210.01570

openalex publication_date 2022/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by Γ'(R), is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are adjacent if and only if x ∉ Ry and y ∉ Rx. In this article, we extend some of the results of [24] to an arbitrary ring. In this connection, we derive a closed-form formula of the Wiener index of the cozero-divisor graph of a finite commutative ring R. As applications, we compute the Wiener index of Γ'(R), when either R is the product of ring of integers modulo n or a reduced ring. At the final part of this paper, we provide a SageMath code to compute the Wiener index of the cozero-divisor graph of these class of rings including the ring ℤ_n of integers modulo n.

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