These notes concern aspects of various graphs whose vertex set is a group $ G $ and
whose edges reflect group structure in some way (so that they are invariant under the action …

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 …

Let S be a (multiplicative) commutative semigroup with 0. Associate to S a (simple) graph G
(S) with vertices the nonzero zero-divisors of S, and two distinct vertices x and y are adjacent …

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 …

This article investigates the concept of dominant metric dimensions in zero divisor graphs
(ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as …

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 T Γ (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 …

Let (Γ,∗) be a finite group and S a possibly empty subset of Γ containing its non-self-
invertible elements. In this paper, we introduce the inverse graph associated with Γ whose …

The unit graph corresponding to an associative ring R is the graph obtained by setting all the
elements of R to be the vertices and defining distinct vertices x and y to be adjacent if and …