Rainbow Connection on Amal(Fn,xz,m) Graphs and Amal(On,xz,m) Graphs

Abstract

Coloring graph is giving a color to a set of vertices and a set of edges on a graph. The condition for coloring a graph is that each color is different for each neighboring member graph. Coloring graph can be done by mapping a different color to each vertex or edge. Rainbow coloring is a type of rainbow connected with coloring edge. It ensures that every graph G has a rainbow path. A rainbow path is a path in a graph where no two vertices have the same color. The minimum number of colors in a rainbow connected graph is called the rainbow connection number denoted by rc(G). The graphs used in this study are the Amal(Fn,xz,m) graph and the Amal(On,xz,m) graph.