Graph Operations and Neighbor Rupture Degree

[摘要] In a communication network, the vulnerability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. A vertex subversion strategy of a graphG, sayS, is a set of vertices inGwhose closed neighborhood is removed fromG. The survival subgraph is denoted byG/S. The neighbor rupture degree ofG,Nr(G), is defined to beNr (G) =max{w(G/S) -|S| - c(G/S): S ⊂ V(G),  w(G/S) ≥1}, whereSis any vertex subversion strategy ofG,w(G/S)is the number of connected components inG/Sandc(G/S)is the maximum order of the components ofG/S(G. Bacak Turan, 2010). In this paper we give some results for the neighbor rupture degree of the graphs obtained by some graph operations.

[学科分类] 应用数学