Graph Operations and Neighbor Rupture Degree

Abstract EN

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.