Semi-strong split domination in graphs

Document Type : Research Paper

Authors

1 Department of Studies in Mathematics, University of Mysore, Mysore-570006 Karnataka, India

2 National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil-626126, India

Abstract

Given a graph $G=(V,E)$‎, ‎a dominating set $D\subseteq V$ is called a semi-strong split dominating set of $G$ if $|V\setminus D|\geq1$ and the maximum degree of the induced subgraph $\langle V\setminus D \rangle$ is $1$‎. ‎The cardinality of a minimum semi-strong split dominating set (SSSDS) of $G$ is the semi-strong split domination number of $G$‎, ‎denoted $\gamma_{sss}(G)$‎. ‎In this paper‎, ‎we introduce the concept and prove several results regarding it‎.

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References

G. Chartrand and L. Lesniak (1996). Graphs $\&$ Digraphs. Third edition, Chapman $\&$ Hall, London. J. F. Fink, M. S. Jacobson, L. Kinch and J. Roberts (1985). On graphs having domination number half their order. Period. Math. Hungar. 16, 287-293 V. R. Kulli and B. Janakiram (1997). The split domination number of a graph. Graph Theory Notes N. Y.. 32, 16-19 V. R. Kulli and B. Janakiram (2006). The strong split domination number of a graph. Acta Cienc. Indica. 32, 715-720 T. W. Haynes, S. T. Hedetniemi and P. J. Slater (1998). Fundamentals of Domination in Graphs. Marcel Dekker, Inc., New York. T. W. Haynes, S. T. Hedetniemi and P. J. Slater (1998). Domination in Graphs: Advanced Topics. Marcel Dekker, Inc., New York. C. Payan and N. H. Xuong (1982). omination-balanced graphs. J. Graph Theory. 6, 23-32

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History

  • Receive Date: 27 September 2013
  • Revise Date: 24 February 2014
  • Accept Date: 16 March 2014
  • Published Online: 01 June 2014

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