Some results on λ-valuation of graphs involving complete bipartite graphs

Abstract

In this paper we show that a graph G obtained from a complete bipartite graph Km,n and a collection of q (≤max\s{m,n\s}) stars Gi by joining the centre of G1 to every vertex of Km, n and joining the centre of Gi to a vertex (not the centre) of Gi+1 (i=1,2,...,q-1) is strongly harmonious. We also prove that a graph obtained from a collection of t complete bipartite graphs Kmi,ni with bipartition (Xi, Yi) by joining exactly one member in Yi with a member in Xi+1 (i=1,2,...,t-1) is strongly c-elegant. The windmill graph K(n) 2,2 of n complete bipartite graphs K2,2 with a common vertex is also shown to be harmonious for all n≥2. © 1991.