Please use this identifier to cite or link to this item:
|Title:||Identities for minors of the Laplacian, resistance and distance matrices|
|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|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.