PRODUCT DISTANCE MATRIX OF A GRAPH AND SQUARED DISTANCE MATRIX OF A TREE

Applicable Analysis and Discrete Mathematics

article

R. B. Bapat¹  S. Sivasubramanian² 

[1] Stat-Math Unit, Indian Statistical Institute;Indian Institute of Technology

关键词: Distance;    trees;    degrees;    block;    line graph;   

DOI  :  10.2298/AADM130415006B

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Let G be a strongly connected, weighted directed graph. We define a productdistance η(i, j) for pairs i, j of vertices and form the corresponding productdistance matrix. We obtain a formula for the determinant and the inverse ofthe product distance matrix. The edge orientation matrix of a directed treeis defined and a formula for its determinant and its inverse, when it exists, isobtained. A formula for the determinant of the (entry-wise) squared distancematrix of a tree is proved.

【 授权许可】

Unknown