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|Title: ||Identities for minors of the Laplacian, resistance and distance matrices|
|Authors: ||BAPAT, RB|
|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.|
|Appears in Collections:||Article|
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