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Upper domination parameters and edge-critical graphs. (English) Zbl 0959.05084

Let \(\pi\) be one of the upper domination parameters \(\beta\), \(\Gamma\) or IR. The authors study graphs for which \(\pi\) decreases (\(\pi\)-edge-critical graphs) whenever an edge is added. They prove characterizations of \(\beta\)- and \(\Gamma\)-edge-critical graphs and show that a graph is IR-edge-critical if and only if it is \(\Gamma\)-edge-critical.

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C75 Structural characterization of families of graphs
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