# Independent transversal domination in graphs

Discussiones Mathematicae Graph Theory (2012)

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

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topIsmail 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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- [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] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
- [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
- [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. Zbl0449.05057

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