Independent transversal domination in graphs

Ismail Sahul Hamid

Discussiones Mathematicae Graph Theory (2012)

  • Volume: 32, Issue: 1, page 5-17
  • ISSN: 2083-5892

Abstract

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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 γ i t ( G ) . In this paper we begin an investigation of this parameter.

How to cite

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Ismail Sahul Hamid. "Independent transversal domination in graphs." Discussiones Mathematicae Graph Theory 32.1 (2012): 5-17. <http://eudml.org/doc/271071>.

@article{IsmailSahulHamid2012,
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 $γ_\{it\}(G)$. In this paper we begin an investigation of this parameter.},
author = {Ismail Sahul Hamid},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {dominating set; independent set; independent transversal dominating set},
language = {eng},
number = {1},
pages = {5-17},
title = {Independent transversal domination in graphs},
url = {http://eudml.org/doc/271071},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Ismail Sahul Hamid
TI - Independent transversal domination in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 1
SP - 5
EP - 17
AB - 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 $γ_{it}(G)$. In this paper we begin an investigation of this parameter.
LA - eng
KW - dominating set; independent set; independent transversal dominating set
UR - http://eudml.org/doc/271071
ER -

References

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  1. [1] G. Chartrand and L. Lesniak, Graphs and Digraphs (Fourth edition, CRC Press, Boca Raton, 2005). Zbl1057.05001
  2. [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. Zbl0447.05039
  3. [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
  4. [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
  5. [5] Topics on Domination, Guest Editors: S.T. Hedetniemi and R.C. Laskar, Discrete Math. 86 (1990). 
  6. [6] E. Sampathkumar and H.B. Walikar, The connected domination number of a graph, J. Math. Phys. Sci. 13 (1979) 607-613. Zbl0449.05057

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