Summary: 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.

05C50, 15A18

normalized Laplacian matrix, eigenvalue, distance