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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/100/14150

Title: Identities for minors of the Laplacian, resistance and distance matrices
Authors: BAPAT, RB
SIVASUBRAMANIAN, S
Keywords: ZETA-FUNCTIONS
COVERINGS
GRAPHS
Issue Date: 2011
Publisher: ELSEVIER SCIENCE INC
Citation: LINEAR ALGEBRA AND ITS APPLICATIONS,435(6)1479-1489
Abstract: 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.
URI: http://dx.doi.org/10.1016/j.laa.2011.03.028
http://dspace.library.iitb.ac.in/jspui/handle/100/14150
ISSN: 0024-3795
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