Solitude number at graphs

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. © 2011 Academic Publications.