Rainbow coloring in some corona product graphs

Rainbow coloring in some corona product graphs

**Authors : **

Kulkarni Sunita Jagannatharao ^{1 *} and R. Murali ^{2}

**Author Address : **

^{1,2} Department of Mathematics, Dr. Ambedkar Institute of Technology Bengaluru, Bengaluru-560056, India.

*Corresponding author.

**Abstract : **

Let $G$ be a non-trivial connected graph on which is defined a coloring $c:E(G) ightarrow{1,2,cdots,k},kin N$ 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 $rc(G)$. In this paper we determine $rc(G)$ for some corona product graphs.

**Keywords : **

Diameter, Edge-coloring Rainbow path, rainbow connection number, Rainbow critical graph, corona product.

**DOI : **

**Article Info : **

*Received : * July 11, 2018; *Accepted : * December 09, 2018.