The rainbow connection number of enhanced power graph

Abstract

Let $G$ be a finite group, the enhanced power graph of $G$, denoted by ${\Gamma }_G^e$, is the graph with vertex set $G$ and two vertices $x,y$ are edge connected in ${\Gamma }_G^e$ if there exist $z\in G$ such that $x,y\in ⟨z⟩$. Let $\zeta$ be a edge-coloring of ${\Gamma }_G^e$. In this article, we calculate the rainbow connection number of the enhanced power graph ${\Gamma }_G^e$.

Cited by in corpus (2)

• Equality of various graphs on finite semigroups
• Enhanced Power Graph of Certain Non-abelian Groups