Rainbow Antimagic Coloring Of Some Graphs

Abstract

Chartrand et al. introduced the idea of rainbow colors in 2008. If every edge on a path P in a graph has a different color, the path is called a rainbow path. If there is at least one rainbow path connecting each pair of vertices in a graph G, then the graph is said to be rainbow connected.  An vertex antimagic-labeling of a graph  is a function  that assigns unique labels to the edges in such a way that the sum of labels (or weights) incident to each edge is different for all edges. When the edge  with weights, defined as , induce an edge coloring and guarantees that there is  a rainbow path between every vertex pair, the graph is said to possess a rainbow antimagic coloring. The minimum number of colors necessary to establish rainbow connectivity under this edge weight assignment is   called the rainbow-antimagic-connection number. In this paper, we determine the rainbow-antimagic-connection number of triangular-snake-graph and double-triangular-snake-graph.