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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta ago. 2019 


Odd harmonious labeling of grid graphs

P. Jeyanthi1

S. Philo2 

Maged Z. Youssef3

1Govindammal Aditanar College for Women, Department of Mathematics, Research Centre, Tiruchendur - 628 215, Tamil Nadu, India

2Manonmaniam Sundaranar University. Research Scholar, Reg.No: 12193, Abishekappatti, Tirunelveli 627012, India. e-mail:

3Imam Mohammad Ibn Saud Islamic University, Department of Mathematics and Statistics, College of Science, Riyad11623, Saudi Arabia. e-mail:


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 Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, vertex union of t copies of Pm×Pn, vertex union of t different copies of Pmᵢ×Pnᵢ 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.

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

Mathematics Subject Classification (2000):  05C78

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The authors thank the referee for the valuable comments to improve the presentation of the paper.


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Received: February 2018; Accepted: November 2018

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