More on Coprime Irregular Graphs
Sankara Narayanan · International Journal of Engineering and Advanced Technology · 2019
An k−edge-weighting of a graph G = (V,E) is a map φ: E(G) → {1,2,3,...k}, where k is a positive integer. Denote Sφ(v) is the sum of edge-weights presenting on the edges incident at the vertex v under the edge-weighting φ. An k−edge-weighting of G is coprime irregular edge-weighting of G if gcd(Sφ(u),Sφ(v)) = 1 for every pair of adjacent vertices u and v in G. A graph G is coprime irregular if G admits a coprime irregular edge-weighting. In this paper, we discuss about coprime irregular edge-weighting for some families of graphs