The rainbow connection number of the power graph of a finite group

Abstract

This paper studies the rainbow connection number of the power graph $\hat{I}{“}_G$ of a finite group $G$. We determine the rainbow connection number of $\hat{I}{“}_G$ if $G$ has maximal involutions or is nilpotent, and show that the rainbow connection number of $\hat{I}{“}_G$ is at most three if $G$ has no maximal involutions. The rainbow connection numbers of power graphs of some nonnilpotent groups are also given.

10 pages, 5 figures, accepted by Graphs and Combinatorics on July 2015