Rainbow Connection Number of Special Graph and Its Operations

Abstract

Let $G$ be a simple graph. An edge-coloring 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 graph and  its operations, namely crown product of $P_{2}$ $\bigodot$ $Pr_{n}$, tensor product of $P_{2}$ $\bigotimes$ $W_{n}$.