Global neighbourhood domination

• Siva Rama Raju, S. V. ^[1] ; Nagaraja Rao, I. H. ^[2]
  1. [1] Ibra College of Technology.
  2. [2] G. V. P. P. G. Courses Visakhapatnam.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 33, Nº. 1, 2014, págs. 25-41
• Idioma: inglés
• DOI: 10.4067/S0716-09172014000100003
• Enlaces
  • Texto completo
• Resumen

  • 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.

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