Graph operations and neighbor rupture degree
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2013
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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, Nr(G), is defined to be Nr (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. © 2013 Saadet Kandİlcİ et al.