Let R be a ring. The prime intersection graph of ideals of R, denoted by G_ P (R) GP (R), is
the graph whose vertex set is the collection of all non-trivial (left) ideals of R with two distinct …

In this paper, it is proved that the complement of the zero-divisor graph of a partially ordered
set is weakly perfect if it has finite clique number, completely answering the question raised …

Let G be a group. In this paper, we introduce and study the intersection subgroup graph of G
as the (simple) graph Γ S (G) with vertices the nontrivial subgroups H of G such that H∩ …

In this paper, connectedness is completely characterized for the complements of the zero-
divisor graphs of partially ordered sets. These results are applied to annihilating ideal …

Abstract Characterization of a finite module with specified number of nontrivial submodules
is one of the most important issues for researchers in module theory. In this paper, we will try …

Let (P,≤) be an atomic poset with the least element 0. The complement of the intersection
graph of ideals of P, denoted by Γ (P), is defined to be a graph whose vertices are all non …

The intersection graph of nontrivial submodules of M, denoted by G (M), is an undirected
simple graph whose vertices are in one-to-one correspondence with all nontrivial …

Let R be a commutative ring and M be a Noetherian R-module. The intersection graph of
annihilator submodules of M, denoted by GA (M) is an undirected simple graph whose …

Let R be a ring with identity and M be a unitary left R-module. The co-intersection graph of
proper submodules of M, Ω (M) is an undirected simple graph whose vertices are non-trivial …

With a finite R-module M we associate a hypergraph CIHR (M) having the set V of vertices
being the set of all nontrivial submodules of M. Moreover, a subset Ei of V with at least two …