Graceful labeling of triangular extension of complete bipartite graph

Sarbari Mitra (Department of Mathematics, Fort Hays State University, 600 Part Street, Hays, KS, 67601)
Soumya Bhoumik (Department of Mathematics, Fort Hays State University, 600 Part Street, Hays, KS, 67601)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications

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