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 …

The zero-divisor graph of a commutative ring R is a simple graph whose vertices are the
nonzero zero divisors of R and two distinct vertices are adjacent if their product is zero. In …

Let R be a ring with non-zero identity. The unit graph of R, denoted by G (R), is an
undirected graph with all the elements of R as vertices and where distinct vertices x, y are …

Let R be a commutative ring with identity and let Z (R, k) be the set of all k-zero-divisors in R
and k> 2 an integer. The k-zero-divisor hypergraph of R, denoted by ℋ k (R), is a hypergraph …

Let R be a commutative ring with identity and let Z (R, k) be the set of all k-zero-divisors in R
and k> 2 an integer. The k-zero-divisor hypergraph of R, denoted by H k (R), is a hypergraph …

Let R be a finite commutative ring with nonzero identity and U (R) be the set of all units of R.
The graph Γ is the simple undirected graph with vertex set R in which two distinct vertices x …

There are so many ways to construct graphs from algebraic structures. Most popular
constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite …

Let R be a commutative ring and Z (R)* be its set of non-zero zero-divisors. The annihilator
graph of a commutative ring R is the simple undirected graph AG (R) with vertices Z (R) …

The most recent advancements in algebra and graph theory enable us to ask a
straightforward question: what practical use does this graph connected with a mathematical …