Graph Operations and Neighbor Rupture Degree. (16th July 2013)

• Record Type: Journal Article
• Authors: Kandİlcİ, Saadet; Bacak-Turan, Goksen; Polat, Refet
• Other Names: Werner Frank Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-07-16
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/836395
• Languages: English
• ISSNs: 1110-757X

Abstract

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.