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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

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

http://dx.doi.org/10.4067/S0716-09172016000400001 

Totally magic cordial labeling of mPn and mKn

 

P. Jeyanthi

Govindamal Aditanar College for Women

N. Angel Benseera

Sri Meenaskshi Government Arts College for Women

India

Ibrahim Cahit

Near East University

Turkey 

 


ABSTRACT

A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V(G) U E(G) → {0,1} such that f (a) + f (b) + f (ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) — nf (1)| ≤ 1, where nf(i) (i = 0, 1) is the sum ofthe number ofvertices and edges with label i. In this paper we establish that mPand mKn are totally magic cordial for various values of m and n.

Keywords : Binary magic total labeling; cordial labeling; totally magic cordial labeling; totally magic cordial deficiency of a graph.

AMS Subject Classification 05C78.


REFERENCES

[1]    I. Cahit, Cordial graphs: A weaker version of graceful and harmonious graphs, Ars Combin, 23, pp. 201-207, (1987).

[2]    I. Cahit, Some totally modular cordial graphs, Discuss. Math. Graph Theory, 22, pp. 247-258, (2002).

[3]    F. Harary, Graph Theory, Addison-Wesley Publishing Co., (1969).

[4]    P. Jeyanthi, N. Angel Benseera and M. Immaculate Mary, On totally magic cordial labeling, SUT Journal ofMathematics, 49 (1), pp. 1318, (2013).

[5]    P. Jeyanthi and N. Angel Benseera, Totally magic cordial labeling of one-point union of n copies of a graph, Opuscula Mathematica, 34 (1), pp. 115-122, (2014).

[6]    P. Jeyanthi and N. Angel Benseera, Totally magic cordial deficiency of some graphs, Utilitas Mathematica, (to appear).

[7]    P. Jeyanthi and N. Angel Benseera, Totally magic cordial labeling of some graphs, Journal ofAlgorithms and Computation, 46 (1), pp. 1-8, (2015).

P. Jeyanthi

Research Centre,

Department of Mathematics,

Govindammal Aditanar College for Women,

Tiruchendur - 628 215, Tamilnadu,

India

e-mail: jeyajeyanthi@rediffmail.com

N. Angel Benseera

Department of Mathematics,

Sri Meenakshi Government Arts College for Women (Autonomous), Madurai-625 002, Tamilnadu,

India

e-mail: angelbenseera@yahoo.com

Ibrahim Cahit

Department of Computer Science and Engineering,

European University of Lefke,

Lefke, Mersin 10,

Turkey

e-mail: ica@lefke.edu.tr

Received : April 2015. Accepted : June 2016

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