The Rainbow (Vertex) Connection Number of Pencil Graphs
Dian N.S. Simamora, A.N.M. Salman · Procedia Computer Science · 2015
An edge colored graph G = ( V ( G ), E ( G )) is said rainbow connected, if any two vertices are connnected by a path whose edges have distinct colors. The rainbow connection number of G , denoted by rc ( G ), is the smallest positive integer of colors needed in order to make G rainbow connected. The vertex-colored graph G is said rainbow vertex-connected, if for every two vertices u and v in V ( G ), there is a u-v path with all internal vertices have distinct color. The rainbow vertex connection number of G , denoted by rvc ( G ), is the smallest number of colors needed in order to make G rainbow vertex-connected. In this paper, we determine rainbow (vertex) connection number of pencil graphs.