Secure domination critical graphs |
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| Authors: | PJP Grobler |
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| Institution: | a Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa
b Department of Mathematics and Statistics, University of Victoria, P. O. Box 3060, Victoria, BC, Canada V8W 3R4 |
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| Abstract: | A secure dominating set X of a graph G is a dominating set with the property that each vertex u∈VG−X is adjacent to a vertex v∈X such that (X−{v})∪{u} is dominating. The minimum cardinality of such a set is called the secure domination number, denoted by γs(G). We are interested in the effect of edge removal on γs(G), and characterize γs-ER-critical graphs, i.e. graphs for which γs(G−e)>γs(G) for any edge e of G, bipartite γs-ER-critical graphs and γs-ER-critical trees. |
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| Keywords: | Secure domination Protection of a graph Edge-removal-critical graph ER-critical graph |
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