Rainbow Connection Number of Prism and Product of Two Graphs

Abstract

An edge-colouring of a graph $G$ is rainbow connected if, for any two vertices of $G$, there are $k$ internally vertex-disjoint paths joining them, each of which is rainbow and then a minimal numbers of color $G$ is required to make rainbow connected. The rainbow connection numbers of a connected graph $G$, denoted $rc(G)$. In this paper we will discuss the rainbow connection number $rc(G)$ for some special graphs and its operations, namely prism graph $P_{m,n}$, antiprism graph $AP_{n}$, tensor product of $C_{3}$ $\bigotimes$ $L_{n}$, joint graph $\bar{K_{3}}$+$C_{n}$.