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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.34 no.1 Antofagasta mar. 2015

http://dx.doi.org/10.4067/S0716-09172015000100001 

Complementary nil vertex edge dominating sets

S. V. Siva Rama Raju

Ibra College of Technology, Sultanate of Oman

I. H. Nagaraja Rao 

G. V. P. College for P. G. Courses, India 

 


ABSTRACT

Dominating sets play a vital role in day-to-day life problems. For-providing effective services in a location, central points are to be identified. This can easily be achieved by graph theoretic techniques. Such graphs and relevant parameters are introduced and extensively studied. One such parameter is complementary nil vertex edge dominating set(cnved-set). A vertex edge dominating set(ved-set) of a connected graph G with vertex set V is said to be a complementary nil vertex edge dominating set(cnved-Set) of G if and only if V — D is not a ved-set of G. A cnved-set of minimum cardinality is called a minimum cnved-set(mcnved-set)of G and this minimum cardinality is called the complementary nil vertex-edge domination number of G and is denoted by γcnve(G). We have given a characterization result for a ved-set to be a cnved-set and also bounds for this parameter are obtained.

Subject Classification: 05C69.

Keywords: Complementary nil vertex edge domination, complementary nil vertex edge domination number, connected domination.


REFERENCES

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[2]    Danut Marcu, A Note On the Domination Number Of a Graph and its Complement. MATHEMATICA BOHEMICA, Vol. 126 (1), pp. 63-65, (2001).         [ Links ]

[3]    T. W.Haynes, S. T. Hedetneimi, P.J. Slater, Fundamentals of Dominations in Graphs, Marcel Dekker, New York, (1988).         [ Links ]

[4]    J. D.Horton, K. Kilakos, Minimum edge dominating sets. SIAM J.Discrete Math., Vol. 6 (3), pp. 375-387, (1993).         [ Links ]

[5]    R. Laskar, K. Peters, Vertex and edge dominating parameters in Graphs. Congr.Numer., Vol. 48, pp. 291-305, (1985).         [ Links ]

[6]    T. Tamizh Chelvam, S. Robinson Chellathurai,Complementary Nil Domination Number of a Graph. Tamkang Journal Of Mathematics., Vol. 40 (2), pp. 165-172, (2009).         [ Links ]

S. V. Siva Rama Raju

Department of Mathematics Ibra College of Technology Ibra, Sultanate of Oman e-mail:shivram2006@yahoo.co.in

I. H. Nagaraja Rao

Department of Mathematics G. V. P. P. G. Courses

Visakhapatnam,India

e-mail:ihnrao@yahoo.com

Received : July 2012. Accepted : September 2014

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