RAINBOW CONNECTION AND STRONG RAINBOW CONNECTION NUMBERS OF

Abstract

A rainbow path in an edge coloring of graph  is a path in which every two edges are assigned different colors. If a nontrivial connected graph  contains a rainbow path for every two vertices in , then  is rainbow-connected. The rainbow connection number  of  is the minimum integer  such that  is rainbow connnected in an edge-coloring with  colors. If a nontrivial connected  contains a rainbow path  geodesic for every two vertices in , then  is strongly rainbow-connected. The strong rainbow connection number  of  is the minimum integer  such that  is strongly rainbow-connected in an edge coloring with  colors. The rainbow connection and strong rainbow connection number of graph , , and  have been found. In this paper, the results will be generalized and the rainbow connection and strong rainbow connection number of graph  will be determined.

 Keywords: rainbow coloring, rainbow connection number, strong rainbow coloring, strong rainbow connection number, graph