The enhanced power graph of a finite group G, denoted by PE(G), is a simple undirected graph whose vertex set is G and two distinct vertices x, y are adjacent if x,y∈⟨z⟩ for some z∈G. In this article, we determine all ...

The large rank of a finite semigroup , denoted by r5( ), is the least number n such that every subset of with n elements generates . Howie and Ribeiro showed that r5( ) = |V| + 1, where V is a largest proper subsemigroup ...

The enhanced power graph Pe(G) of a group G is a simple undirected graph with vertex set G and two distinct vertices x,y are adjacent if both x and y belongs to same cyclic subgroup of G. In this paper, we obtain various ...

The commuting graph Δ(G) of a finite non-abelian group G is a simple graph with vertex set G, and two distinct vertices x, y are adjacent if xy=yx. In this paper, first we discuss some properties of Δ(G). We determine the ...

Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by Γ'(R), is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are ...

The enhanced power graph Pe(S) of a semigroup S is a simple graph whose vertex set is S and two vertices x,y∈S are adjacent if and only if x,y∈⟨z⟩ for some z∈S, where ⟨z⟩ is the subsemigroup generated by z. In this paper, ...

The intersection ideal graph Γ(S) of a semigroup S is a simple undirected graph whose vertices are all nontrivial left ideals of S and two distinct left ideals I,J are adjacent if and only if their intersection is nontrivial. ...

Since the work of Marczewski [10], many authors have studied the rank properties in the context of general algebras (cf. [1–3,9,11,12,14]). The concept of rank for general algebras is analogous to the concept of dimension ...