Distances in weighted trees and group inverse of Laplacian matrices

被引：49
|
作者：
Kirkland, SJ
Neumann, M
Shader, BL
机构：
[1] UNIV CONNECTICUT,DEPT MATH,STORRS,CT 06269
[2] UNIV WYOMING,DEPT MATH,LARAMIE,WY 82071
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1997年 / 18卷 / 04期
关键词：
Laplacian matrix; generalized inverse; weighted tree;
D O I：
10.1137/S0895479896298713
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：827 / 841
页数：15
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