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 …

Suppose that R is a commutative ring with identity. Let A (R) be the set of all ideals of R with
non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG (R) with …

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 ring with unity and I (R)* be the set of all nontrivial left ideals of R. The intersection
graph of ideals of R, denoted by G (R), is a graph with the vertex set I (R)* and two distinct …

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 …

Let R be a commutative ring and 𝔸 (R) be the set of ideals with non-zero annihilators. The
annihilating-ideal graph of R is defined as the graph 𝔸𝔾 (R) with the vertex set 𝔸 (R)*= 𝔸 …

Let R be a commutative ring with nonzero identity, and let Z (R) be its set of zero-divisors.
The total graph of R is the (undirected) graph T (Γ (R)) with vertices all elements of R, and …

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 …

This work is based on ideas of Ilić [A. Ilić, The energy of unitary Cayley graphs, Linear
Algebra Appl. 431 (2009) 1881–1889] on the energy of unitary Cayley graph. For a finite …

Let R be a ring with unity. The inclusion ideal graph of a ring R, denoted by In (R), is a graph
whose vertices are all nontrivial left ideals of R and two distinct left ideals I and J are …