Special Classes of Coprime Irregular Graphs

Abstract

: An k-edge-weighting of a graph G = (V, E) is a mapping : E(G) {1, 2, 3, ...k}, where k is a positive integer. The sum of the edge-weighting appearing on the edges incident at the vertex v under the edge-weighting and is denoted by (v). An k edge-weighting of G is a coprime irregular edge-weighting if gcd ( (u), (v)) = 1 for every pair of adjacent vertices u and v in G. A graph G admits a coprime irregular edge-weighting is called a coprime irregular graph. In this paper, we discuss the coprime irregular edge-weighting for some special classes of graphs.