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.