Rainbow coloring in some corona product graphs

Abstract

Let $G$ be a non-trivial connected graph on which is defined a coloring $c: E(G) \rightarrow\{1,2, \cdots, k\}, k \in N$ of the edges of $G$, where adjacent edges may be colored the same. A path $P$ in $G$ is called a rainbow path if no two edges of $P$ are colored the same. $G$ is said to be rainbow-connected if for every two vertices $u$ and $v$ in it, there exists a rainbow $u-v$ path. The minimum $k$ for which there exist such a $k$-edge coloring is called the rainbow connection number of $G$, denoted by $r c(G)$. In this paper we determine $r c(G)$ for some corona product graphs.