Abstract:Kemeny's constant of a simple connected graph G is the expected length of a random walk from i to any given vertex j = i. We provide a simple method for computing Kemeny's constant for 1-separable via effective resistance methods from electrical network theory. Using this formula, we furnish a simple proof that the path graph on n vertices maximizes Kemeny's constant for the class of undirected trees on n vertices. Applying this method again, we simplify existing expressions for the Kemeny's constant of barbel… Show more
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