TITLE:
Vertex-Neighbor-Scattering Number Of Trees
AUTHORS:
Zongtian Wei, Yong Liu, Anchan Mai
KEYWORDS:
Vertex-Neighbor-Scattering Number, Tree, Path, Star, Comet
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.1 No.4,
July
26,
2011
ABSTRACT: 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.