ELA, Volume 8, pp. 94-109, June 2001, abstract.

An upper bound on algebraic connectivity of 
graphs with many cutpoints
                
S. Kirkland

Let G be a graph on n vertices which has k cutpoints. 
A tight upper bound on the algebraic connectivity of G 
in terms of n and k for the case that k > n/2 is provided; 
the graphs which yield equality in the bound are also 
characterized. This completes an investigation initiated 
by the author in a previous paper, which dealt with the 
corresponding problem for the case that k <= n/2.