Distance matrix and Laplacian of a tree with attached graphs

被引：18

作者：

Bapat, RB ^{[1
]}

机构：

[1] Indian Stat Inst, Delhi Ctr, New Delhi 110016, India

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 411卷

关键词：

tree; distance matrix; resistance distance; Laplacian matrix; determinant; transportation problem;

D O I：

10.1016/j.laa.2004.06.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：295 / 308

页数：14

共 25 条

[1]

Bapat R.B., 2000, CONT MATH, V259, P45

[2]

Bapat R. B., 1999, Mathematics Student, V68, P87

[3]

Bapat RB., 1999, Linear Multilinear Algebra, V46, P299, DOI DOI 10.1080/03081089908818623

[4]

Bapat RB., 1997, Encyclopedia of mathematics and its applications, V64

[5]

BAPAT RB, 2004, MATCH COMMUN MATH CO, V50, P73

[6]

BAPAT RB, IN PRESS LINEAR ALGE, DOI DOI 10.1016/J.6AA.2004.05.011

[7]

BENISRAEL A, 1974, GEN INVERSES THEORY

[8]

BOLOOBAS B, 1998, MODERN GRAPH THEORY

[9]

Campbell SL, 1979, GEN INVERSES LINEAR

[10] A COMBINATORIAL PROOF OF THE ALL MINORS MATRIX TREE THEOREM [J].

CHAIKEN, S .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1982, 3 (03) :319-329

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