Journal of Applied Mathematics
Volume 2013 (2013), Article ID 836395, 7 pages
Research Article

Graph Operations and Neighbor Rupture Degree

1Department of Mathematics, Yasar University, 35100 Izmir, Turkey
2Department of Mathematics, Celal Bayar University, 45140 Manisa, Turkey

Received 25 March 2013; Revised 13 June 2013; Accepted 14 June 2013

Academic Editor: Frank Werner

Copyright © 2013 Saadet Kandİlcİ et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 , say , is a set of vertices in whose closed neighborhood is removed from . The survival subgraph is denoted by . The neighbor rupture degree of , , is defined to be , where is any vertex subversion strategy of , is the number of connected components in and is the maximum order of the components of (G. Bacak Turan, 2010). In this paper we give some results for the neighbor rupture degree of the graphs obtained by some graph operations.