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Graphs with given connectivity and independence number or networks with given measures of vulnerability and survivability

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2 Author(s)

The criterion for invulnerability of a network based on the connectivity of a graph is well treated in literature. We define a criterion for survivability of a network in terms of the independence number of a graph. The following problems are then considered. 1) Find an r -connected graph, with n vertices and m_0 = [(nr + l)/2] edges, whose independence number is the minimum possible, where [x] denotes the greatest integer less than or equal to x \cdot 2 ) Given positive integers n,m,r , and k , find the realizability conditions for a graph with n vertices and m edges, whose connectivity is at least r and independence number is at most k .

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Circuit Theory, IEEE Transactions on  (Volume:20 ,  Issue: 1 )