The Smith normal form of product distance matrices
R. B. Bapat; Sivaramakrishnan Sivasubramanian
Special Matrices (2016)
- Volume: 4, Issue: 1, page 46-55
- ISSN: 2300-7451
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topR. B. Bapat, and Sivaramakrishnan Sivasubramanian. "The Smith normal form of product distance matrices." Special Matrices 4.1 (2016): 46-55. <http://eudml.org/doc/276949>.
@article{R2016,
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.},
author = {R. B. Bapat, Sivaramakrishnan Sivasubramanian},
journal = {Special Matrices},
language = {eng},
number = {1},
pages = {46-55},
title = {The Smith normal form of product distance matrices},
url = {http://eudml.org/doc/276949},
volume = {4},
year = {2016},
}
TY - JOUR
AU - R. B. Bapat
AU - Sivaramakrishnan Sivasubramanian
TI - The Smith normal form of product distance matrices
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 46
EP - 55
AB - 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.
LA - eng
UR - http://eudml.org/doc/276949
ER -
References
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