  In this paper, we determine a formula for Kemeny's constant for a graph with
multiple bridges, in terms of quantities that are inherent to the subgraphs
obtained upon removal of all bridges and that can be computed independently.
With the formula, we consider several optimization problems for Kemeny's
constant for graphs with bridges, and we remark on the computational benefit of
this formula for the computation of Kemeny's constant. Finally, we discuss some
potential applications.
