In this paper, we associate a simple graph to a lattice L, in which the vertex

set is being the set of all elements of L, and two distinct vertices x and y are adjacent

if x ∨ y ∈ S, when S is a multiplicatively ...

Let R be a ring with the identity element 1, α be an endomorphism of R and b be a

left α-derivation. In this paper, we introduce a generalization of a commuting graph,

which is denoted by ΓR(α, b), as a ...

Let R be a commutative ring with nonzero identity. We denote by AG(R)

the annihilator graph of R,whose vertex set consists of the set of nonzero zero-divisors

of R, and two distint vertices x and y are adjacent ...

Let (P,≤) be a partially ordered set with a least element 0. The regular digraph of ideals of P, denoted by

\\gama (P), is a digraph whose vertex-set is the set of all nontrivial ideals of P and, for every two ...

Let R be a commutative ring with identity element. For a

natural number n, we associate a simple graph, denoted by

Gamma^n_R , with R^n setminus { as the vertex set and two

distinct vertices X and Y ...

Let R be a commutative ring, I(R) be the set of all ideals of R and S be a subset of I^*(R) = I(R) -{0}

We define a Cayley sum digraph of ideals of R, denoted by Cay^+(I(R),S) as a directed graph whose

vertex ...

Let R be a commutative ring with nonzero identity and J(R) be the Jacobson radical

of R. The Jacobson graph of R, denoted by JR, is a graph with vertex-set R \\ J(R), such that

two distinct vertices a and b ...

In this paper, we investigate when the unit, unitary and total graphs have

planar line graph, and also we study the case when these line graphs are ring graph or

outerplanar.

Let G be a finite non-abelian group and g be a fixed element of G. In 2014, Tolue et al. introduced the g-noncommuting graph of G (denoted by $\\Gamma_G^g$) with vertex set G and two distinct vertices x and y join by an ...

Let R be a commutative ring. The regular digraph

of ideals of R, denoted by \\gama(R), is a digraph whose vertex-set is

the set of all non-trivial ideals of R and, for every two distinct

vertices I and ...