Rainbow Connection Number of Rocket Graphs

All graphs in this paper are simple, unite, and undirected. The concept of rainbow coloring was introduced by Chartrand et al`. Let G be a non trivial connected graph. Fork E N, we define a coloring r: E(G) -> (1,2...,k) of the edges of G such that the adjacent can be colored the same. A path P in G is a rainbow path if no two edges of P are colored the same. A path connecting two vertices u and v in G is called u v path. A graph G is said rainbow -connected if for every two vertices u and v of G, there exist a rainbow u v path. In this case, the coloring c is called the rainbow k -coloring of G. The minimum k such that G has rainbow k -coloring is called the rainbow connection number of G. Clearly that dium(G) <= rc(G) where diam(G) denotes the diameter of G. in this paper we determine the rainbow connection number of rocket graphs.