Smith Normal Form of a distance matrix inspired by the four-point condition

Authors

R. B. Bapat, Indian Statistical Institute (Delhi Centre)
Sivaramakrishnan Sivasubramanian, Indian Institute of Technology Bombay

Article Type

Research Article

Publication Title

Linear Algebra and Its Applications

Abstract

The four point theorem is a condition for distances to arise from trees. Based on this condition, for any tree T on n vertices, we associate an (n2)×(n2) matrix MT. We find the rank and the Smith Normal Form (SNF) of the matrix MT and show that it only depends on n and is independent of the structure of the tree T. Curiously, the non-zero part of the SNF of MT coincides with the SNF of the distance matrix of T. Many such “tree independent” results are known and this result is yet another such result.

First Page

301

Last Page

312

DOI

10.1016/j.laa.2020.05.035

Publication Date

10-15-2020

Comments

Open Access, Bronze

Recommended Citation

Bapat, R. B. and Sivasubramanian, Sivaramakrishnan, "Smith Normal Form of a distance matrix inspired by the four-point condition" (2020). Journal Articles. 104.
https://digitalcommons.isical.ac.in/journal-articles/104