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Vertex-Neighbor-Scattering Number Of Trees

Author(s): Zongtian Wei | Yong Liu | Anchan Mai

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 01;
Issue: 04;
Start page: 160;
Date: 2011;
Original page

Keywords: Vertex-Neighbor-Scattering Number | Tree | Path | Star | Comet

A vertex subversion strategy of a graph G=(V,E) is a set of vertices S V(G) whose closed neighborhood is deleted from G . The survival subgraph is denoted by G/S . We call S a cut-strategy of G if G/S is disconnected, or is a clique, or is φ . The vertex-neighbor scattering number of G is defined to be VNS(G)=max{ω(G/S)-|S|} , where S is any cut-strategy of G , and ω(G/G) is the number of the components of G/S . It has been proved that the computing problem of this parameter is NP–complete, so we discuss the properties of vertex-neighbor-scattering number of trees in this paper.
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