Bapat, R. B.
(2006)
*Determinant of the distance matrix of a tree with matrix weights*
Linear Algebra and its Applications, 416
(1).
pp. 2-7.
ISSN 0024-3795

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

Related URL: http://dx.doi.org/10.1016/j.laa.2005.02.022

## Abstract

Let T be a tree with n vertices and let D be the distance matrix of T. According to a classical result due to Graham and Pollack, the determinant of D is a function of n, but does not depend on T. We allow the edges of T to carry weights, which are square matrices of a fixed order. The distance matrix D of T is then defined in a natural way. We obtain a formula for the determinant of D, which involves only the determinants of the sum and the product of the weight matrices.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Tree; Distance Matrix; Laplacian Matrix; Matrix Weights; Determinant |

ID Code: | 81587 |

Deposited On: | 07 Feb 2012 05:11 |

Last Modified: | 07 Feb 2012 05:11 |

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