ELA, Volume 16, pp. 204-207, August 2007, abstract.
A Note on a Distance Bound Using Eigenvalues of the
Normalized Laplacian Matrix
Steve Kirkland
Let G be a connected graph, and let X and Y be subsets
of its vertex set. A previously published bound is considered
that relates the distance between X and Y to the eigenvalues
of the normalized Laplacian matrix for G, the volumes of X
and Y, and the volumes of their complements. A counterexample
is given to the bound, and then a corrected version of the
bound is provided.