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Direct Calculation of a Tree Length Using a Distance Matrix

✍ Scribed by Yves Pauplin


Book ID
105933522
Publisher
Springer
Year
2000
Tongue
English
Weight
796 KB
Volume
51
Category
Article
ISSN
0022-2844

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## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _

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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