Graceful labeling of triangular extension of complete bipartite graph

Abstract

For positive integers m, n, K m,n represents the complete bipartite graph. We name the graph G = K m,n ⊙ K2 as triangular extension of complete bipartite graph K m,n , since there is a triangle hanging from every vertex of K m,n . In this paper we show that G is graceful when m = n = 2ℓ, for any integer ℓ.