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Distances in Weighted Trees and Group Inverse of Laplacian Matrices

journal contribution
posted on 01.10.1997, 00:00 by S. J. Kirkland, M. Neumann, Bryan L. Shader
In this paper we find formulas for group inverses of Laplacians of weighted trees. We then develop a relationship between entries of the group inverse and various distance functions on trees. In particular, we show that the maximal and minimal entries on the diagonal of the group inverse correspond to certain pendant vertices of the tree and to a centroid of the tree, respectively. We also give a characterization for the group inverses of the Laplacian of an unweighted tree to be an M-matrix.

History

ISO

eng

Language

English

Publisher

University of Wyoming. Libraries

Journal title

SIAM Journal on Matrix Analysis and Applications

Collection

Faculty Publication - Department of Mathmatics & Statistics