Four-point condition matrices of edge-weighted trees

Author:

Azimi Ali1,Jana Rakesh2,Nagar Mukesh K.3,Sivasubramanian Sivaramakrishnan2

Affiliation:

1. Department of Mathematics and Applied Mathematics, Xiamen University Malaysia , 43900 Sepang , Selangor Darul Ehsan , Malaysia

2. Department of Mathematics, Indian Institute of Technology, Bombay , Mumbai 400 076 , India

3. Department of Mathematics, BITS Pilani , K. K. Birla Goa Campus , Goa 403 726 , India

Abstract

Abstract Formulas for the determinant of distance matrix D T {D}_{T} of tree T T are known in the unweighted case and in the case when the edges of T T have commuting variable weights. Associated with the four-point condition (4PC) and a tree T T are two matrices, the Max4PC T {{\rm{Max4PC}}}_{T} and the Min4PC T {{\rm{Min4PC}}}_{T} . These are not full rank matrices and their rank, a basis B B , and formulas for the determinant when restricted to the rows and columns of B B are known. In this work, we generalize both these matrices to the case when the edges of T T have commuting variable weights and determine edge-weighted counterparts of known results.

Publisher

Walter de Gruyter GmbH

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3