Geodesic
Domination parameters of a graph with deleted special subset of edges
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 2, pp. 229-238.

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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.
Keywords: domination parameters, edge deleted graphs 
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Kwaśnik, Maria; Zwierzchowski, Maciej. Domination parameters of a graph with deleted special subset of edges. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 2, pp. 229-238. http://geodesic.mathdoc.fr/item/DMGT_2001_21_2_a7/

[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.