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Squared distance matrices of trees with matrix weights
- Publication Year :
- 2022
-
Abstract
- Let $T$ be a tree on $n$ vertices whose edge weights are positive definite matrices of order $s$. The squared distance matrix of $T$, denoted by $\Delta$, is the $ns \times ns$ block matrix with $\Delta_{ij}=d(i,j)^2$, where $d(i,j)$ is the sum of the weights of the edges in the unique $(i,j)$-path. In this article, we obtain a formula for the determinant of $\Delta$ and find ${\Delta}^{-1}$ under some conditions.<br />Comment: Preliminary version. Comments are welcome. 17 pages
- Subjects :
- Mathematics - Combinatorics
05C22, 05C50
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2205.01734
- Document Type :
- Working Paper