# Domination parameters of a graph with deleted special subset of edges

Maria Kwaśnik; Maciej Zwierzchowski

Discussiones Mathematicae Graph Theory (2001)

- Volume: 21, Issue: 2, page 229-238
- ISSN: 2083-5892

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topMaria Kwaśnik, and Maciej Zwierzchowski. "Domination parameters of a graph with deleted special subset of edges." Discussiones Mathematicae Graph Theory 21.2 (2001): 229-238. <http://eudml.org/doc/270223>.

@article{MariaKwaśnik2001,

abstract = {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.},

author = {Maria Kwaśnik, Maciej Zwierzchowski},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination parameters; edge deleted graphs; split domination number; maximal domination number},

language = {eng},

number = {2},

pages = {229-238},

title = {Domination parameters of a graph with deleted special subset of edges},

url = {http://eudml.org/doc/270223},

volume = {21},

year = {2001},

}

TY - JOUR

AU - Maria Kwaśnik

AU - Maciej Zwierzchowski

TI - Domination parameters of a graph with deleted special subset of edges

JO - Discussiones Mathematicae Graph Theory

PY - 2001

VL - 21

IS - 2

SP - 229

EP - 238

AB - 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.

LA - eng

KW - domination parameters; edge deleted graphs; split domination number; maximal domination number

UR - http://eudml.org/doc/270223

ER -

## References

top- [1] R. Diestel, Graph Theory (Springer-Verlag New York, Inc., 1997).
- [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. Zbl0681.05020
- [3] V.R. Kulli and B. Janakiram, The maximal domination number of a graph, Graph Theory Notes of New York XXXIII (1997) 11-13.
- [4] V.R. Kulli and B. Janakiram, The split domination number of a graph, Graph Theory Notes of New York XXXII (1997) 16-19.
- [5] M. Kwaśnik and M. Zwierzchowski, Special kinds of domination parameters in graphs with deleted edge, Ars Combin. 55 (2000) 139-146.
- [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. Zbl0696.05029

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