Protection of a network by complete secure domination
Abstract
A complete secure dominating set of a graph G is a dominating set D \subseteq V(G) with the property that for each v \in D, there exists F={ vj | vj \in N(v) \cap (V(G)-D)} such that for each vj \in F, ( D-{v }) \cup { vj } is a dominating set. The minimum cardinality of any complete secure dominating set is called the complete secure domination number of G and is denoted by \gamacsd(G). In this paper, the bounds for complete secure domination number for some standard graphs like grid graphs and stacked prism graphs in terms of number of vertices of G are found and also the bounds for the complete secure domination number of a tree are obtained in terms of different parameters of G.
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