Determinant of the distance matrix of a tree with matrix weights

被引：23
作者：
Bapat, RB [1 ]
机构：
[1] Indian Stat Inst, New Delhi 110016, India
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 416卷 / 01期
关键词：
tree; distance matrix; Laplacian matrix; matrix weights; determinant;
D O I：
10.1016/j.laa.2005.02.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：2 / 7
页数：6
相关论文
共 50 条
  • [1] Product distance matrix of a tree with matrix weights
    Bapat, R. B.
    Sivasubramanian, Sivaramakrishnan
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 468 : 145 - 153
  • [2] The distance matrix of a tree with weights on its arcs
    Zhou, Hui
    Ding, Qi
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 511 : 365 - 377
  • [3] The product distance matrix of a tree with matrix weights on its arcs
    Zhou, Hui
    Ding, Qi
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 499 : 90 - 98
  • [4] A q-analoque of the distance matrix of a tree with matrix weights
    Barik, Sasmita
    Mondal, Madhab
    Pan, Sirshendu
    LINEAR & MULTILINEAR ALGEBRA, 2024,
  • [5] THE DISTANCE MATRIX OF A BIDIRECTED TREE
    Bapat, R. B.
    Lal, A. K.
    Pati, Sukanta
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2009, 18 : 233 - 245
  • [6] A q-analogue of the distance matrix of a tree
    Bapat, R. B.
    Lal, A. K.
    Pati, Sukanta
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 416 (2-3) : 799 - 814
  • [7] Distance matrix and Laplacian of a tree with attached graphs
    Bapat, RB
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 411 : 295 - 308
  • [8] On distance and Laplacian matrices of trees with matrix weights
    Atik, Fouzul
    Kannan, M. Rajesh
    Bapat, Ravindra B.
    LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (14) : 2607 - 2619
  • [9] The bipartite distance matrix of a nonsingular tree
    Bapat, R. B.
    Jana, Rakesh
    Pati, S.
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 631 : 254 - 281
  • [10] Squared distance matrix of a weighted tree
    Bapat, Ravindra B.
    ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS, 2019, 7 (02) : 301 - 313
12345