In this book, we introduce several graphical representations of a ring. In the past three
decades, graphs constructed from algebraic structures have been studied extensively by …

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 …

Let R be a commutative ring with nonzero identity and H be a nonempty proper subset of R
such that R\H is a saturated multiplicatively closed subset of R. The generalized total graph …

Let R be a commutative ring and Z (R) be its set of all zero-divisors. The total graph of R,
denoted by TΓ (R), is the undirected graph with vertex set R, and two distinct vertices x and y …

In this paper, we discuss some recent results on graphs attached to rings. In particular, we
deal with comaximal graphs, unit graphs, and total graphs. We then define the notion of …

The algebraic polynomial plays a significant role in mathematical chemistry to compute the
exact expressions of distance‐based, degree‐distance‐based, and degree‐based …

We study the total graph of a finite commutative ring. We calculate its metric dimension in the
case when the Jacobson radical of the ring is nontrivial, and we examine the metric …

Let R be a commutative ring with nonzero unity. Let Z (R) be the set of all zerodivisors of R.
The total graph of R, denoted by T (Γ (R)), is the simple graph with vertex set R and two …

Let R be a commutative ring, U (R) be the set of all unit elements of R, G be a multiplicative
subgroup of U (R) and S be a non-empty subset of G such that S− 1={s− 1: s∈ S}⫅ S. In [16] …

Let R be a finite commutative ring with 1≠ 0. In this article, we study the total graph of R,
denoted by τ (R), determine some of its basic graph-theoretical properties, determine when it …