IJPAM: Volume 66, No. 3 (2011)


Harika Guler$^1$, Pinar Dundar$^2$, Mehmet Ali Balci$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Science
Ege University
Bornova, Izmir, 35100, TURKEY
$^1$e-mail: harikaguler@hotmail.com
$^2$e-mail: pinar.dundar@ege.edu.tr
$^3$e-mail: mehmet.ali.balci@ege.edu.tr

Abstract.The vulnerability is one of the most important notion in network design. Vulnerability can be considered as the resistance of the network after any breakdown in its nodes or links. Since any network can be modeled by a graph, vulnerability parameters on graphs also work on network types. In this work we defined and examined the solitude number of a connected graph as a new global vulnerability parameter. Described parameter was examined at basic graph classes and under graph operations, also an algorithm which calculates the solitude number of general graph, was given.

Received: December 18, 2010

AMS Subject Classification: 05C85, 05C07, 05C76

Key Words and Phrases: graph theory, vulnerability, solitude number at graphs

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 3