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 and I be a proper ideal

of R. The annihilator graph of R with respect to I, which is denoted by AGI (R), is the

undirected graph with vertex-set V(AGI (R)) ...

Let R be a commutative ring with non-zero identity. We describe all C3- and C4-free intersection graphs of non-trivial ideals of R as well as Cn-free intersection graph when R is a reduced ring. Also, we shall describe all ...