Identities for minors of the Laplacian, resistance and distance matrices

Bapat, R. B. ; Sivasubramanian, Sivaramakrishnan (2011) Identities for minors of the Laplacian, resistance and distance matrices Linear Algebra and its Applications, 435 (6). pp. 1479-1489. ISSN 0024-3795

Full text not available from this repository.

Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.laa.2011.03.028

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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Laplacian; Distance Matrix; Resistance Matrix; Determinant; Partitioned Matrix; q-analogue
ID Code:81599
Deposited On:07 Feb 2012 05:14
Last Modified:07 Feb 2012 05:14

Repository Staff Only: item control page