Moore-Penrose inverse of distance Laplacians of trees are Z matrices
R. Balaji, Vinayak Gupta
TL;DR
This paper proves that the Moore-Penrose inverse of the distance Laplacian matrix of a tree has non-positive off-diagonal entries, revealing a specific matrix property related to tree structures.
Contribution
It establishes a new property of the Moore-Penrose inverse of distance Laplacian matrices for trees, contributing to matrix theory and graph analysis.
Findings
Off-diagonal entries are non-positive in the Moore-Penrose inverse
Property holds for all trees
Enhances understanding of matrix properties in graph theory
Abstract
We show that all off-diagonal entries in the Moore-Penrose inverse of the distance Laplacian matrix of a tree are non-positive.
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Taxonomy
TopicsGraph theory and applications · Matrix Theory and Algorithms · Topological and Geometric Data Analysis