Neighbor integrity of transformation graphs

In a communication network, the vulnerability measures are essential to guide the designer in choosing an appropriate topology. They measure the stability of the network to disruption of operation after the failure of certain stations or communication links. If a station or operative is captured in a spy network, then the adjacent stations will be betrayed and are therefore useless in the whole network. In this sense, Margaret B. Cozzens and Shu-Shih Y. Wu modeled a spy network as a graph and then defined the neighbor integrity of a graph to obtain the vulnerability of a spy network [10]. The neighbor integrity of a graph G, is defined to be $NI(G)=\displaystyle{\min-{S\subseteq V(G)}\{|S|+c(G/S)\}}$, where S is any vertex subversion strategy of G and c(G/S) is the maximum order of the components of G/S. In this paper, we investigate the transformation graphs G-+-, G+-, G ++-, G- -, G+-+, G-++, G -+ and G+++ of a graph G, and determine their neighbor integrity. © 2013 World Scientific Publishing Company.