Vertex-Neighbor-Scattering Number Of Trees

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.

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.

Cite this paper

nullZ. Wei, Y. Liu and A. Mai, "Vertex-Neighbor-Scattering Number Of Trees,"*Advances in Pure Mathematics*, Vol. 1 No. 4, 2011, pp. 160-162. doi: 10.4236/apm.2011.14029.

nullZ. Wei, Y. Liu and A. Mai, "Vertex-Neighbor-Scattering Number Of Trees,"

References

[1] Z. Wei, A. Mai and M. Zhai, “Vertex-Neighbor-Scattering Number of Graphs,” Ars Combinatoria, Vol. 102, 2011.

[2] F. Li and X. Li, “Computational Complexity and Bounds for Neighbor-Scattering Number of Graphs,” 8th International Symposium on Parallel Architectures, Algorithms and Net-works, Las Vegas, 7-9 December 2005, pp. 478-483. doi:10.1109/ISPAN.2005.30

[3] J. A. Bondy and U. S. R. Murty, “Graph Theory with Applications,” Macmillan, London, 1976

[1] Z. Wei, A. Mai and M. Zhai, “Vertex-Neighbor-Scattering Number of Graphs,” Ars Combinatoria, Vol. 102, 2011.

[2] F. Li and X. Li, “Computational Complexity and Bounds for Neighbor-Scattering Number of Graphs,” 8th International Symposium on Parallel Architectures, Algorithms and Net-works, Las Vegas, 7-9 December 2005, pp. 478-483. doi:10.1109/ISPAN.2005.30

[3] J. A. Bondy and U. S. R. Murty, “Graph Theory with Applications,” Macmillan, London, 1976