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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.1 Antofagasta mar. 2019 


Odd harmonious labeling of super subdivisión graphs

P. Jeyanthi1 

S. Philo2 

M. K. Siddiqui3 

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

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

3COMSATS University Islamabad, Sahiwal Campus, Department of Mathematics, Pakistan. 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 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.

Keywords : harmonious labeling; odd harmonious labeling; super subdivision of graphs

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Received: December 2015; Accepted: November 2018

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