On the (Strong) Rainbow Vertex Connection of Graphs Resulting from Edge Comb Product
Dafik Dafik, Slamin Slamin, Agustina Muharromah · Journal of Physics Conference Series · 2018
The vertex-colored graph G = ( V, E ) is said rainbow vertex-connected, if for every two vertices u and v in V , 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 required in order to make graph G to be rainbow vertex-connected. If every two vertices u and v in V are connected by at least one shortest rainbow path, then G is strongly rainbow vertex-connected. The strong rainbow vertex- connection number, denoted by srvc ( G ), is the minimum number of colors required in order make graph G to be strongly rainbow vertex-connected. In this paper, we determine the rainbow vertex connection number and the strong rainbow vertex connection number of graphs which are resulted from edge comb product.