Strong rainbow vertex-connection of cubic graphs

The rainbow vertex - connection number, rvc(G), of a connected graph is the minimum number of colors needed to color its vertices such that every pair of vertices is connected by at least one path whose internal vertices have distinct colors. Rainbow coloring has received much attention recently in the field of interconnection networks. Computing the rainbow connection number of a graph is NP- hard and it finds its applications in the secure transfer of classified information between agencies and in cellular network. In this paper we characterize some families of cubic graphs and its strong rainbow connection numbers have been found.