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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.4 Antofagasta dic. 2016

http://dx.doi.org/10.4067/S0716-09172016000400004 

Some results on skolem odd difference mean labeling

 

P. Jeyanthi

Govindammal Aditanar College for Women

R. Kalaiyarasi 

Dr. Sivanthi Aditanar College of Engineering

D. Ramya

Government Arts College for Women

T. Saratha Devi

G. Venkataswamy Naidu College

India 


ABSTRACT

Let G = (V, E) be a graph with p vertices and q edges. A graph G is said to be skolem odd difference mean if there exists a function f : V(G) → {0, 1, 2, 3,...,p+3q — 3} satisfying f is 1-1 and the induced map f * : E(G) →{1, 3, 5,..., 2q-1} defined by f * (e) = [(f(u)-f(v))/2] is a bijection. A graph that admits skolem odd difference mean labeling is called skolem odd difference mean graph. We call a skolem odd difference mean labeling as skolem even vertex odd difference mean labeling if all vertex labels are even. A graph that admits skolem even vertex odd difference mean labeling is called skolem even vertex odd difference mean graph.

In this paper we prove that graphs B(m,n) : Pw, (PmõSn), mPn, mPn U tPs and mK 1,n U tK1,s admit skolem odd difference mean labeling. If G(p, q) is a skolem odd differences mean graph then p≥ q. Also, we prove that wheel, umbrella, Bn and Ln are not skolem odd difference mean graph.

Keywords : Skolem difference mean labeling, skolem odd difference mean labeling, skolem odd difference mean graph, skolem even vertex odd difference mean labeling, skolem even vertex odd difference mean graph.

AMS Subject Classification: 05C78.


REFERENCES

[1]    F. Harary, Graph theory, Addison Wesley, Massachusetts, (1972).

[2]    Joseph A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, (2015),         [ Links ] #DS6.

[3]    K. Manickam and M. Marudai, Odd mean labelings of graphs, Bulletin ofPure and Applied Sciences, 25E (1), pp. 149-153, (2006).         [ Links ]

[4]    K. Murugan, A. Subramanaian, Skolem difference mean labeling of H-graphs, International Journal ofMathematics and Soft Computing, 1, (1), pp. 115-129, (2011).         [ Links ]

[5]    D. Ramya and M. Selvi, On skolem difference mean labeling of some trees, International Journal ofMathematics and Soft Computing, 4 (2), pp. 11-18, (2014).         [ Links ]

[6]    D. Ramya, M. Selvi and R. Kalaiyarasi, On skolem difference mean labeling of graphs, International Journal of Mathematical Archive, 4 (12), pp. 73-79, (2013).         [ Links ]

[7]    D. Ramya, R. Kalaiyarasi and P. Jeyanthi, On skolem odd difference mean labeling of graphs, Journal ofAlgorithms and Computing, (45), pp. 1-12, (2014).         [ Links ]

[8]    S. Somasundaram and R. Ponraj, Mean labelings of graphs, National Academy Science Letter, (26), pp. 210-213, (2003).         [ Links ]

P. Jeyanthi

Research Centre,

Department of Mathematics,

Govindammal Aditanar College for Women, Tiruchendur-628215, Tamilnadu,

India

e-mail : jeyajeyanthi@rediffmail.com

R. Kalaiyarasi

Department of Mathematics,

Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628215, Tamilnadu,

India

e-mail : 2014prasanna@gmail.com D. Ramya

Department of Mathematics,

Government Arts College for Women, Ramanathapuram, Tamilnadu,

India

e-mail : aymar_padma@yahoo.co.in

T. Saratha Devi

Department of Mathematics,

G. Venkataswamy Naidu College, Kovilpatti-628502, Tamilnadu,

India

e-mail : rajanvino03@gmail.com

 

Received : November 2015. Accepted : October 2016

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