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Further results on the common neighbourhood domination and some related graphs

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In this paper we obtain some results and bounds on the common neighbourhood domination number (CN-domination number) of a graph G. Also we introduce the common neighbourhood domatic number (CN-domatic number). Common neighbourhood connectedness(CN-connectedness), Common neighbourhood regularity (CN-regularity), Common neighbourhood completeness (CN-completeness) are introduce by define the CN-connected graph, CN-regular graph, CN-complete garph and CN-complement. Some properties and interesting results of these graphs are established.

Abstract

In this paper we obtain some results and bounds on the common neighbourhood domination number (CN-domination number) of a graph G. Also we introduce the common neighbourhood domatic number (CN-domatic number). Common neighbourhood connectedness(CN-connectedness), Common neighbourhood regularity (CN-regularity), Common neighbourhood completeness (CN-completeness) are introduce by define the CN-connected graph, CN-regular graph, CN-complete garph and CN-complement. Some properties and interesting results of these graphs are established.

참고문헌 (12)

  1. ANWAR ALWARDI, "Totally connected domination in graphs", Advanced Studies in Contemporary Mathematics, 22(4), pp.557~563 (2012), 장전수학회
  2. Anwar Alwardi, "On the Common neighbourhood domination number", Journal Of Computer And Mathematical Sciences, 2(3) (2011)
  3. ANWAR ALWARDI, "THE P3-DOMINATION IN GRAPHS", Advanced Studies in Contemporary Mathematics, 23(1), pp.181~192 (2013), 장전수학회
  4. S. Arumugam, "Neighborhood connected and neighborhood total domination in graphs", Proc. Int. Conf. on Disc. Math., 2334 B, pp.45~51 (2008)
  5. B. Chaluvaraju, "Some parameters on neighborhood number of a graph", Electronic Notes of Discrete Mathematics, 33, pp.139~146 (2009)
  6. E. J. Cockayne, "Towards a theory of dominationin graphs", Networks, 7, pp.247~261 (1977)
  7. F. Harary, "Graph theory" (1969), Addison-Wesley
  8. T. W. Haynes, "Fundamentals of domination in graphs" (1998), Marcel Dekker, Inc.
  9. S. M. Hedetneimi, "Disjoint dominating sets in graphs", Proc. Int. Conf. on Disc.Math., IMI-IISc, pp.88~101 (2006)
  10. V. R. Kulli, "Further results on the neighborhood number of a graph", Indian J. Pure and Appl. Math, 23(8), pp.575~577 (1992)
  11. E. Sampathkumar, "The neighborhood number of a graph", Indian J. Pure and Appl. Math, 16(2), pp.126~132 (1985)
  12. H. B. Walikar, "Recent developmentsin the theory of domination in graphs", Mehta Research instutute, Alahabad, MRI Lecture Notes in Math, 1 (1979)

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