DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 21(1) (2001) 229-238
DOI: 10.7151/dmgt.1146

DOMINATION PARAMETERS OF A GRAPH WITH
DELETED SPECIAL SUBSET OF EDGES

Maria Kwaśnik and Maciej Zwierzchowski

Institute of Mathematics
Technical University of Szczecin
al. Piastów 48/49, 70-310 Szczecin, Poland
e-mail: kwasnik@arcadia.tuniv.szczecin.pl
e-mail: mzwierz@arcadia.tuniv.szczecin.pl

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.

Keywords: domination parameters, edge deleted graphs.

2000 Mathematics Subject Classification: 05C69.

References

[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.
[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.

Received 5 December 2000
Revised 7 September 2001