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The analysis of vulnerability in
graphs generally involves some questions
about how the underlying graph is connected. If we think of the graph as
modeling a network, vulnerability measure the resistance of the network to
disruption of operation after the failure of
certain stations. Many parameters in
graph theory have been used in the past to describe communication network, stability or vulnerability. Several of these deal with two fundamental questions
about the resulting graph. How many vertices can still communicate? How
difficult is it to reconnect the graph? In this paper we introduce some important vulnerability parameters in graphs and
prove some new theorems about tenacity.
These theorems show the relation
between tenacity and other vulnerability parameters.