Global neighbourhood domination
DOI:
https://doi.org/10.4067/S0716-09172014000100003Keywords:
Global neighbourhood domination, global neighbourhood domination number, global domination, restrained domination, connected domination, dominación de entorno global, número de dominación de entorno global, dominación global, dominación restringida.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, n — 1,n — 2, n.References
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[2] R. C. Brigham, R. D. Dutton,On Neighbourhood Graphs, J. Combin. inform. System Sci, 12, pp. 75-85, (1987).
[3] G. S. Domke, etal., Restrained Domination in Graphs, Discrete Mathematics, 203, pp. 61-69, (1999).
[4] T. W. Haynes, S. T. Hedetneimi, P. J. Slater, Fundamentals of Dominations in Graphs Marcel Dekker, New York, (1988).
[5] I. H. Naga Raja Rao, S. V. Siva Rama Raju, On Semi-Complete Graphs, International Journal Of Computational Cognition, Vol.7(3), pp. 50-54, (2009).
[6] D. F. Rall, Congr. Numer., 80, pp. 89-95, (1991).
[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).
Published
2017-03-23
How to Cite
[1]
S. V. Siva Rama Raju and I. H. Nagaraja Rao, “Global neighbourhood domination”, Proyecciones (Antofagasta, On line), vol. 33, no. 1, pp. 25-41, Mar. 2017.
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