Distance matrix and Laplacian of a tree with attached graphs

Bapat, R. B. (2005) Distance matrix and Laplacian of a tree with attached graphs Linear Algebra and its Applications, 411 . pp. 295-308. 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.2004.06.017


A tree with attached graphs is a tree, together with graphs defined on its partite sets. We introduce the notion of incidence matrix, Laplacian and distance matrix for a tree with attached graphs. Formulas are obtained for the minors of the incidence matrix and the Laplacian, and for the inverse and the determinant of the distance matrix. The case when the attached graphs themselves are trees is studied more closely. Several known results, including the Matrix Tree theorem, are special cases when the tree is a star. The case when the attached graphs are paths is also of interest since it is related to the transportation problem.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Tree; Distance Matrix; Resistance Distance; Laplacian Matrix; Determinant; Transportation Problem
ID Code:78313
Deposited On:19 Jan 2012 06:33
Last Modified:19 Jan 2012 06:33

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