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Discussiones Mathematicae Graph Theory 32(1) (2012)
5-17
DOI: https://doi.org/10.7151/dmgt.1581
Independent Transversal Domination in Graphs
| Ismail Sahul Hamid
Department of Mathematics |
Abstract
A set S ⊆ V of vertices in a graph G = (V, E) is called a dominating set if every vertex in V−S is adjacent to a vertex in S. A dominating set which intersects every maximum independent set in G is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by γit(G). In this paper we begin an investigation of this parameter.
Keywords: dominating set, independent set, independent transversal dominating set
2010 Mathematics Subject Classification: 05C.
References
| [1] | G. Chartrand and L. Lesniak, Graphs and Digraphs (Fourth edition, CRC Press, Boca Raton, 2005). |
| [2] | E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211--219, doi: 10.1002/net.3230100304. |
| [3] | T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). |
| [4] | T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). |
| [5] | Topics on Domination, Guest Editors: S.T. Hedetniemi and R.C. Laskar, Discrete Math. 86 (1990). |
| [6] | E. Sampathkumar and H.B. Walikar, The connected domination number of a graph, J. Math. Phys. Sci. 13 (1979) 607--613. |
Received 19 October 2009
Revised 10 September 2010
Accepted 17 December 2010
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