Given a commutative ring R with identity 1≠ 0, let the set Z (R) denote the set of zero-
divisors and let Z*(R)= Z (R)\{0} be the set of non-zero zero-divisors of R. The zero-divisor …

The Wiener index of the zero-divisor graph of Zn - ScienceDirect Skip to main contentSkip to
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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 …

For a simple connected graph G of order n, we obtain the distance signless Laplacian
spectrum of the joined union of regular graphs G 1, G 2,…, G n in terms of their adjacency …

Let R be a ring with unity. The upper ideal relation graph Γ U (R) of the ring R is the simple
undirected graph whose vertex set is the set of all non-unit elements of R and two distinct …

Let R be a commutative ring with Z∗(R) as the set of nonzero zero divisors. The zero divisor
graph of R, denoted by Γ (R), is the graph whose vertex set is Z∗(R), where two distinct …

Let Z (R) be the set of zero-divisors of a commutative ring R with non-zero identity and
Z*(R)= Z (R)∖{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R …

Let R be a commutative ring with identity. The zero-divisor graph of R denoted by Γ (R) is an
undirected graph Γ (R)=(V (Γ), E (Γ)), where V (Γ) is the set of non-zero zero-divisors of R …

Let $ R $ be a commutative ring with unity $1\ne 0$. In this paper, we completely describe
the vertex and the edge chromatic number of the compressed zero divisor graph of the ring …

In chemistry, graph theory has been widely utilized to address molecular problems, with
numerous applications in graph theory and ring theory within this field. One of these …