Identities for minors of the Laplacian, resistance and distance matrices
DSpace at IIT Bombay
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Title |
Identities for minors of the Laplacian, resistance and distance matrices
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Creator |
BAPAT, RB
SIVASUBRAMANIAN, S |
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Subject |
ZETA-FUNCTIONS
COVERINGS GRAPHS Laplacian Distance matrix Resistance matrix Determinant Partitioned matrix q-Analogue |
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Description |
It is shown that if L and D are the Laplacian and the distance matrix of a tree respectively, then any minor of the Laplacian equals the sum of the cofactors of the complementary submatrix of D. up to sign and a power of 2. An analogous, more general result is proved for the Laplacian and the resistance matrix of any graph. A similar identity is proved for graphs in which each block is a complete graph on r vertices, and for q-analogues of such matrices of a tree. Our main tool is an identity for the minors of a matrix and its inverse. (C) 2011 Elsevier Inc. All rights reserved.
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Publisher |
ELSEVIER SCIENCE INC
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Date |
2012-06-26T07:35:38Z
2012-06-26T07:35:38Z 2011 |
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Type |
Article
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Identifier |
LINEAR ALGEBRA AND ITS APPLICATIONS,435(6)1479-1489
0024-3795 http://dx.doi.org/10.1016/j.laa.2011.03.028 http://dspace.library.iitb.ac.in/jspui/handle/100/14150 |
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Language |
English
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