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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.33 no.1 Antofagasta Mar. 2014

http://dx.doi.org/10.4067/S0716-09172014000100003 

 

Global neighbourhood domination

 

S. V. Siva Rama Raju
Ibra College of Technology, Sultanate of Oman

 

I. H. Nagaraja Rao
G. V. P. P. G. Courses, India


ABSTRACT

A subset D of vertices of a graph G is called a global neighbourhood dominating set(gnd - set) if D is a dominating set for both G and GN, where GN is the neighbourhood graph of G. The global neighbourhood domination number(gnd - number) is the minimum cardinality of a global neighbourhood dominating set of G and is denoted by γ gn(G). In this paper sharp bounds for γ gn, are supplied for graphs whose girth is greater than three. Exact values ofthis number for paths and cycles are presented as well. The characterization result for a subset ofthe vertex set of G to be a global neighbourhood dominating set for G is given and also characterized the graphs of order n having gnd -numbers 1, 2, n1,n — 2, n.

Subject Classification : 05C69.

Keywords : Global neighbourhood domination, global neighbourhood domination number, global domination, restrained domination, connected domination.


 

REFERENCES

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[7] E. Sampathkumar, H. B. Walikar,The connected Domination Number of a Graph, J. Math. Phy. Sci, Vol.13, pp. 607-613, (1979).

[8] E. Sampathkumar,The global domination number of a graph, J. Math.Phy. Sci, Vol. 23 (5), (1989).

 

S. V. Siva Rama Raju
Department of Mathematics Ibra College of Technology Ibra,
Sultanate of Oman
e-mail :shi_vram2006@yahoo.co.in

 

I. H. Nagaraja Rao
Department of Mathematics G. V. P. P. G. Courses Visakhapatnam, India
e-mail : ihnrao@yahoo.com

Received : September 2012. Accepted : October 2013.

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