Document Type

Article

Publication Date

10-1-1997

Abstract

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.

Publication Title

SIAM Journal on Matrix Analysis and Applications

DOI

10.1137/S0895479896298713

Included in

Mathematics Commons

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