Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498141 | Linear Algebra and its Applications | 2005 | 14 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
R.B. Bapat,