Odd harmonious labeling of grid graphs

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2019-03-0027

Keywords:

Harmonious labeling, Odd harmonious labeling, Grid graph, Path union of graphs, One point union of path of graphs, t-super subdivision of graphs

Abstract

A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) ? {0, 1, 2, · · · , 2q ? 1} such that the induced function f* : E(G) ? {1, 3, · · · , 2q ? 1} defined by f? (uv) = f (u) + f (v) is a bijection. In this paper we prove that path union of t copies of Pm×Pn, path union of t different copies of Pm?×Pn? where 1 ? i ? t, vertex union of t copies of Pm×Pn, vertex union of t different copies of Pm?×Pn? where 1 ? i ? t, one point union of path of Ptn (t.n.Pm×Pm), t super subdivision of grid graph Pm×Pn are odd harmonious graphs.

Author Biographies

P. Jeyanthi, Govindammal Aditanar College for Women.

Department of Mathematics. Research Centre.

S. Philo, Manonmaniam Sundaranar University.

Research Scholar.

Maged Z. Youssef, Imam Mohammad Ibn Saud Islamic University.

Department of Mathematics and Statistics, College of Science.

References

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Published

2019-08-06

How to Cite

[1]
P. Jeyanthi, S. Philo, and M. Z. Youssef, “Odd harmonious labeling of grid graphs”, Proyecciones (Antofagasta, On line), vol. 38, no. 3, pp. 411-428, Aug. 2019.

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