Gracefulness of Cycle of Cycles and Cycle of Complete Bipartite Graphs

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 12 | Number 1 | Year 2014 | Article Id. IJMTT-V12P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V12P503

Gracefulness of Cycle of Cycles and Cycle of Complete Bipartite Graphs

V J Kaneria, H M Makadia, Meera Meghapara

Abstract

In this paper we prove that cycle of cycles C(Cn1,Cn2,. . . ,Cnt) is graceful, when t ≡ 0 (mod 2), ni ≡ 0 (mod 4) (1 ≤ i ≤ t) and Σt/2i=1 ni = Σti=t/2 ni. We also prove that cycle of the complete bipartite graph C(tKm,n) (t is an even integer) is graceful and C(tCn) is cordial, ∀t; n ∈ N - {1, 2}

Keywords

Graceful labeling, Cordial labeling, Cycle of cycles and cycle of complete bipartite graphs.

References

[1] J. A. Gallian, The Electronics Journal of Combinatorics, 19, ]DS6(2013).
[2] F. Harary, Graph theory Addition Wesley, Massachusetts, 1972.
[3] V. J. Kaneria, H. M. Makadia and M. M. Jariya, Graceful labeling for cycle of graphs, Int. J. of Math. Res., vol-6(2), (2014), pp. 135 - 139.
[4] A. Rosa, On certain valuation of graph, Theory of Graphs (Rome, July 1966), Goden and Breach, N. Y. and Paris, 1967, 349-355.

Citation :

V J Kaneria, H M Makadia, Meera Meghapara, "Gracefulness of Cycle of Cycles and Cycle of Complete Bipartite Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 1, pp. 19-26, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V12P503