Graph Operations and Neighbor Rupture Degree. (16th July 2013) - Kandİlcİ, Saadet; Bacak-Turan, Goksen; Polat, Refet
Abstract : 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 graph G, say S, is a set of vertices in G whose closed neighborhood is removed from G . The survival subgraph is denoted by G / S . The neighbor rupture degree of G, N r ( G ), is defined to be N r   ( G )   = max { w ( G / S )   - | S |   -   c ( G / S ) :   S   ⊂   V ( G ),     w ( G / S )   ≥ 1 }, where S is any vertex subversion strategy of G, w ( G / S ) is the number of connected components in G / S and c ( G / S ) is the maximum order of the components of G / 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.