PDF
DOMINATION PARAMETERS OF A GRAPH WITH
Discussiones
Mathematicae Graph Theory 21(1) (2001) 229-238
DOI: https://doi.org/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
Close