A Simple Method for Computing Kemeny's Constant for 1-separable Graphs

A 1-Separation Formula for the Graph Kemeny Constant and Braess Edges

We provide a simple method for computing the expected length of a random walk from to any given vertex for 1-separable graphs via effective resistance methods from electrical network theory.We also simplify existing expressions for the expected length of a random walk from to any given vertex of barbell graphs and demonstrate which barbell maximizes the expected length of a random walk from to any given vertex.Finally, we generalize the notion of the braess edge to a collection of non-edges in a graph such that their addition to the base graph increases the expected length of a random walk from to any given vertex.