Rainbow coloring in some corona product graphs

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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.



Article Info :

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



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