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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

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


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


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.



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


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

Received : September 2012. Accepted : October 2013.

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