This article presents a survey of results consisting of the Wiener index of graphs associated
with commutative rings. In particular, we focus on zero-divisor graphs, unit graphs, total …

arXiv:2305.06270v1 [math.AC] 10 May 2023 Page 1 arXiv:2305.06270v1 [math.AC] 10 May
2023 GRAPH RINGS AND IDEALS: WOLMER VASCONCELOS CONTRIBUTIONS MARIA VAZ …

For a finite group G and a subset X∅ of G, the commuting graph, indicated by G= C (G, X), is
the simple connected graph with vertex set X and two distinct vertices x and y are edge …

The study on graphs emerging from different algebraic structures such as groups, rings,
fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and …

Let R be a commutative ring with identity and let (x) be the principal ideal generated by x∈
R. Let Ω (R)∗ be the set of all nontrivial principal ideals of R. The reduced cozero-divisor …

The normalized distance Laplacian matrix of a connected graph G, denoted by D 𝓛 (G), is
defined by D 𝓛 (G)= Tr (G)− 1/2 DL (G) Tr (G)− 1/2, where D (G) is the distance matrix, the DL …

Zero-divisor graphs have been a key area of focus for many researchers. For the semi local
ring R of finite cartesian product of finite fields, we consider the zero divisor graph of R …

The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is
the set of zero-divisors in the ring, with a and b adjacent if ab= 0. We show that the class of …

In this study, we define the structure formation of the annihilator monic prime graph of
commutative rings, whose distinct vertices X and J satisfies a condition ann XJ≠ ann X⋃ …

Let G be a group. In this paper, we introduce and study the intersection subgroup graph of G
as the (simple) graph Γ S (G) with vertices the nontrivial subgroups H of G such that H∩ …