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

-connected graph, with

vertices and
![m_0 = [(nr + l)/2]](/images/tex/10953.gif)
edges, whose independence number is the minimum possible, where
![[x]](/images/tex/5218.gif)
denotes the greatest integer less than or equal to

) Given positive integers

, and

, find the realizability conditions for a graph with

vertices and

edges, whose connectivity is at least

and independence number is at most

.