The co-maximal subgroup graph Γ (G) of a group G is a graph whose vertices are non-trivial
proper subgroups of G and two vertices H and K are adjacent if HK= G. In this paper, we …

In this sequel paper, we continue our study on co-maximal subgroup graph Γ (G) of a group
G. We discuss some further results on connectedness and when Γ (G) is edgeless …

The co-maximal subgroup graph $\Gamma (G) $ of a group $ G $ is a graph whose vertices
are non-trivial proper subgroups of $ G $ and two vertices $ H $ and $ K $ are adjacent if …

Let H be a group. The co-maximal graph of H, denoted by Γ (H), is a graph whose vertices
are nontrivial elements of H and two distinct vertices x and y are adjacent in Γ (H) if and only …

In this paper, we provide some conditions of (super)-solvability and nilpotency of a finite
group $ G $ based on its number of subgroups $ Sub (G) $. Our results generalize the …

In this communication, the co-maximal subgroup graph $\Gamma (G) $ of a finite group $ G
$ is examined when $ G $ is a finite nilpotent group, finite abelian group, dihedral group …

Let R be a commutative ring with identity. The co-maximal ideal graph of R, denoted by Γ
(R), is a simple graph whose vertices are proper ideals of R which are not contained in the …

In this paper, we introduce a new graph called prime order element graph\(\Gamma (G)\)
defined on a finite group G. Its set of vertices is the group G and two distinct vertices\(x, y\in …

Let $ R $ be a commutative ring with identity $1\neq 0$ which admits atleast two maximal
ideals. In this article, we have studied simple, undirected graph $(\operatorname …

Let $ G $ be a group and $ S $ be the collection of all non-trivial proper subgroups of $ G $.
The co-maximal subgroup graph $\Gamma (G) $ of a group $ G $ is defined to be a graph …