Distances in Weighted Trees and Group Inverse of Laplacian Matrices
journal contributionposted on 15.11.2021, 21:40 authored 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.
PublisherUniversity of Wyoming. Libraries
Journal titleSIAM Journal on Matrix Analysis and Applications
CollectionFaculty Publication - Department of Mathmatics & Statistics
- Library Sciences - LIBS