Odd harmonious labeling of super subdivisión graphs.

Authors

Keywords:

Harmonious labeling, Odd harmonious labeling, Super subdivision of graphs

Abstract

A graph G(p, q) is said to be odd harmonious if there exists an injection ????: V (G) ? {0, 1, 2, · · · , 2q ? 1} such that the induced function ????? : E(G) ? {1, 3, · · · , 2q ? 1} defined by ?????(uv) = ???? (u) + ???? (v) is a bijection. In this paper we prove that super subdivision of any cycle Cm with m ? 3 ,ladder, cycle Cn for n ? 0(mod 4) with K1,m and uniform fire cracker are odd harmonious graphs.

Author Biographies

P. Jeyanthi, Govindammal Aditanar College for Women.

Department of Mathematics, Research Centre.

M. K. Siddiqui, COMSATS University Islamabad.

Sahiwal Campus, Department of Mathematics.

References

J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronics Journal of Combinatorics, (2017), # DS6.

R. L. Graham and N. J. A. Sloane, On Additive bases and Harmonious Graphs, SIAM J. Algebr. Disc. Meth., 4, pp. 382-404, (1980).

F. Harary, Graph Theory, Addison-Wesley, Massachusetts, (1972).

Z. Liang, Z. Bai, On the Odd Harmonious Graphs with Applications, J. Appl. Math. Comput., 29, pp. 105-116, (2009).

P. Jeyanthi, S. Philo and Kiki A. Sugeng, Odd harmonious labeling of some new families of graphs, SUT Journal of Mathematics, Vol. 51, No. 2, pp. 53-65, (2015).

P. Jeyanthi, S. Philo, Odd Harmonious Labeling of Some Cycle Related Graphs, Proyecciones Journal of Mathematics, Vol. 35, No. 1, pp. 85-98, (2016).

P. Jeyanthi, S. Philo, Odd Harmonious Labeling of Plus Graphs, Bulletin of the International Mathematical Virtual Institute, Vol. 7, pp. 515—526, (2017).

P. Jeyanthi, S. Philo, Maged Z. Youssef, Odd Harmonious Labeling of Grid Graphs, Proyecciones Journal of Mathematics, to appear.

P. Selvaraju, P. Balaganesan and J. Renuka, Odd Harmonious Labeling of Some Path Related Graphs, International J. of Math. Sci. and Engg. Appls., 7 (III), pp. 163-170, (2013).

S. K. Vaidya and N. H. Shah, Some New Odd Harmonious Graphs, International Journal of Mathematics and Soft Computing, 1, pp. 9-16, (2011).

S. K. Vaidya, N. H. Shah, Odd Harmonious Labeling of Some Graphs, International J. Math. Combin., 3, pp. 105-112, (2012).

Published

2019-02-25

How to Cite

[1]
P. Jeyanthi, S. Philo, and M. K. Siddiqui, “Odd harmonious labeling of super subdivisión graphs.”, Proyecciones (Antofagasta, On line), vol. 38, no. 1, pp. 1-11, Feb. 2019.

Issue

Section

Artículos