Domination parameters of a graph with deleted special subset of edges
Maria Kwaśnik ; Maciej Zwierzchowski
Discussiones Mathematicae Graph Theory, Tome 21 (2001), p. 229-238 / Harvested from The Polish Digital Mathematics Library
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This paper contains a number of estimations of the split domination number and the maximal domination number of a graph with a deleted subset of edges which induces a complete subgraph Kₚ. We discuss noncomplete graphs having or not having hanging vertices. In particular, for p = 2 the edge deleted graphs are considered. The motivation of these problems comes from [2] and [6], where the authors, among other things, gave the lower and upper bounds on irredundance, independence and domination numbers of an edge deleted graph.

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:270223 
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Maria Kwaśnik; Maciej Zwierzchowski. Domination parameters of a graph with deleted special subset of edges. Discussiones Mathematicae Graph Theory, Tome 21 (2001) pp. 229-238. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1146/

[000] [1] R. Diestel, Graph Theory (Springer-Verlag New York, Inc., 1997).

[001] [2] F. Harary and S. Schuster, Interpolation theorems for the independence and domination numbers of spanning trees, Ann. Discrete Math. 41 (1989) 221-228, doi: 10.1016/S0167-5060(08)70462-X. | Zbl 0681.05020

[002] [3] V.R. Kulli and B. Janakiram, The maximal domination number of a graph, Graph Theory Notes of New York XXXIII (1997) 11-13.

[003] [4] V.R. Kulli and B. Janakiram, The split domination number of a graph, Graph Theory Notes of New York XXXII (1997) 16-19.

[004] [5] M. Kwaśnik and M. Zwierzchowski, Special kinds of domination parameters in graphs with deleted edge, Ars Combin. 55 (2000) 139-146.

[005] [6] T.W. Haynes, L.M. Lawson, R.C. Brigham and R.D. Dutton, Changing and unchanging of the graphical invariants: minimum and maximum degree, maximum clique size, node independence number and edge independence number, Cong. Numer. 72 (1990) 239-252. | Zbl 0696.05029