The neighbour-scattering number can be computed in polynomial time for interval graphs
Computers & Mathematics with Applications
The size of a minimum critically m-neighbor-scattered graph
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
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Let G = (V,E) be a graph. A vertex subversion strategy of G, X, is a set of vertices of G whose closed neighborhood is deleted from G. The survival-subgraph is de- fined by G/X. A vertex subversion strategy of G, X, is called a cut-strategy of G if the survival-subgraph is disconnected, or a clique, or \emptyset. The neighbor-scattering number of G, S(G), is defined as S(G) = max{w(G/X) - |X|: X is a cut-stragey of G w(G/X) \ge 1}, where w(G/X) is the number of connected componentsin the graph G/X. As a new graphic parameter, neighbor-scattering number can be used to measure the vulnerability of spy networks. In this paper, we prove that the problem of computing the neighbor-scattering number of a graph is NP-complete and discuss the upper and lower bounds for the neighbor-scattering number via some other well-known graphic parameters. Finally, we give formulas for the neighbor-scattering numbers of the join and union of two disjoint graphs.