Kemeny's constant for a graph with bridges

Abstract: 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.