SciELO - Scientific Electronic Library Online

 
vol.35 número1The forcing open monophonic number of a graphCoupled lower and upper solution approach for the existence of Solutions of nonlinear coupled system with nonlinear coupled boundary conditions índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google

Compartir


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.1 Antofagasta mar. 2016

http://dx.doi.org/10.4067/S0716-09172016000100006 

Proyecciones Journal of Mathematics Vol. 35, No 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


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.


REFERENCES

[1]    M. E. Abdel-Aal, Odd Harmonious Labelings of Cyclic Snakes, International Journal on applications of Graph Theory in Wireless Adhoc networks and Sensor Networks, 5 (3), pp. 1-13, (2013).         [ Links ]

[2]    M. E. Abdel-Aal, New Families of Odd Harmonious Graphs, International Journal of Soft Computing, Mathematics and Control, 3 (1), pp. 1-13, (2014).         [ Links ]

[3]    J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronics Journal of Combinatorics, (2015) #DS6.         [ Links ]

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

[5]    A. Gusti Saputri, K. A. Sugeng and D. Froncek, The Odd Harmonious Labeling of Dumbbell and Generalized Prism Graphs, AKCE Int. J. Graphs Comb., 10 (2), pp. 221-228, (2013).         [ Links ]

[6]    F. Harary, Graph Theory, Addison-Wesley, Massachusetts, (1972).         [ Links ]

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

[8]    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).         [ Links ]

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

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

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

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

Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons