Graceful labeling of triangular extension of complete bipartite graph

Sarbari Mitra, Soumya Bhoumik


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.


graceful labeling, bipartite graph, corona

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A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (International Symposium Rome) (1966), 349–355.

G. Sethuraman and A. Elumalai, On graceful graphs: pendant edge extensions of a family of complete bipartite and complete tripartite graphs, Indian J. Pure Appl. Math. 32 (9) (2001), 1283–1296.

J.A. Bondy, and U.S.R. Murty, Graph Theory, Springer, New York, (2008).

J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. (2017), #DS6.

K.J. Ma, Graceful Graphs, Beijing University Publishing House, Beijing, (1991).

M. Maheo, H. Thuillier, On d-graceful graphs, Ars Combin. 13 (1982), 181–192.

P.J. Slater, On k-graceful graphs. In Proc. of the 13th SE Conf. on Combinatorics, Graph Theory and Computing (1982), 53–57.

R.L. Graham, N.J. Sloane, On additive bases and harmonious graphs, SIAM Journal on Al- gebraic Discrete Methods 1(4) (1980), 382–404.

S. Bhoumik and S. Mitra, Graceful labeling of pendant edge extension of complete bipartite graph, International Journal of Mathematical Analysis 8 (58) (2014), 2885–2897.

S. Mitra and S. Bhoumik, On graceful labeling of 1-crown for complete bipartite graph, International Journal of Computational and Applied Mathematics 10 (1) (2015) 69–75.

S.W. Golomb, How to number a graph, Graph Theory and Computing, (1972), 23–37.

W. Li, G. Li, and Q. Yan, Advances in computer science, environment, ecoinformatics, and education, Communications in Computer and Information Science 214 (2011), 297–301.

Y.L. Jirimuta, On k-gracefulness of r-crown Ir(K1,n)(n ≥ 2,r ≥ 2) for complete bipartite graph, Journal of Inner Mongolia University for Nationalities 2 (2003), 108–110.


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