The Smith normal form of product distance matrices
R. B. Bapat ; Sivaramakrishnan Sivasubramanian
Special Matrices, Tome 4 (2016), p. 46-55 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:276949 
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     title = {The Smith normal form of product distance matrices},
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     volume = {4},
     year = {2016},
     pages = {46-55},
     zbl = {1338.15073},
     language = {en},
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R. B. Bapat; Sivaramakrishnan Sivasubramanian. The Smith normal form of product distance matrices. Special Matrices, Tome 4 (2016) pp. 46-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0005/

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