Rainbow Coloring of Three New Graph Classes

Abstract

Let G be a simple, finite, and connected graph. A path in an edge colored graph is said a rainbow path, if no two edges on the path have the same color. The graph G is called a rainbow-connected, if any two vertices are connected by a rainbow path. An edge-coloring of such G is rainbow coloring. The rainbow connection number rc(G) of G is the smallest number of colors needed in order to make G rainbow connected. In this paper, we introduce three new graph classes, namely tunjung graphs, sandat graphs, and jempiring graphs. We determine the rainbow connection number of the graphs.