The Smith normal form of product distance matrices

Authors

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

Article Type

Research Article

Publication Title

Special Matrices

Abstract

Let G = (V, E) be a connected graph with 2-connected blocks H1, H2, . . . , Hr. Motivated by the exponential distance matrix, Bapat and Sivasubramanian in [4] defined its product distance matrix DG and showed that det DG only depends on det DHi for 1 ≤ i ≤ r and not on the manner in which its blocks are connected. In this work, when distances are symmetric, we generalize this result to the Smith Normal Form of DG and give an explicit formula for the invariant factors of DG.

First Page

45

Last Page

55

DOI

10.1515/spma-2016-0005

Publication Date

1-1-2016

Comments

Open Access; Gold Open Access

Recommended Citation

Bapat, R. B. and Sivasubramanian, Sivaramakrishnan, "The Smith normal form of product distance matrices" (2016). Journal Articles. 4489.
https://digitalcommons.isical.ac.in/journal-articles/4489