Proyecciones Journal of Mathematics Vol. 35, N^o 1, pp. 85-98, March 2016. Universidad Católica del Norte Antofagasta - Chile

Odd harmonious labeling of some cycle related graphs

P. Jeyanthi

Govindammal Aditanar College for Women

S. Philo

PSN College of Engineering and Technology

India

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ABSTRACT

A graph G(p, q) is said to be odd harmonious if there exists an in-jection 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. A graph that admits odd harmonious labeling is called odd harmonious graph. In this paper we prove that any two even cycles sharing a common vertex and a common edge are odd harmonious graphs.

Keywords : Harmonious labeling; odd harmonious labeling; odd harmonious graph; strongly odd harmonious labeling; strongly odd harmonious graph.

AMS Subject Classification (2010) : 05C78.

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P. Jeyanthi

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

India

e-mail: jeyajeyanthi@rediffmail.com

S. Philo

Department of Mathematics,

PSN College of Engineering and Technology, Melathediyoor,

Tirunelveli, Tamil Nadu,

India

e-mail: lavernejudia@gmail.com

Received : May 2015. Accepted : December 2015