The number of P-vertices for acyclic matrices with given nullity

被引：0
|
作者：
Du, Zhibin [1 ]
da Fonseca, Carlos M. [2 ,3 ]
机构：
[1] South China Normal Univ, Sch Software, Foshan 528225, Guangdong, Peoples R China
[2] Kuwait Coll Sci & Technol, Block 4,POB 27235, Safat 13133, Kuwait
[3] Univ Deusto, Chair Computat Math, Bilbao 48007, Spain
来源：
DISCRETE MATHEMATICS | 2023年 / 346卷 / 12期
基金：
中国博士后科学基金;
关键词：
P-vertices; Acyclic matrices; Trees; Eigenvalues; Nullity; Continuity; MULTIPLICITIES; EIGENVALUES;
D O I：
10.1016/j.disc.2023.113592
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we completely characterize those trees on n vertices for which there is a singular matrix with nullity k and the number of P-vertices is n - k -1 or n - k - 2. The characterization of acyclic matrices, with rank r and the number of P-vertices is r -1, or with odd rank r and the number of P-vertices is r - 2, was first investigated in Fonseca et al. (2021) [10]. Here we introduce a unified method to revisit those results, and further cover the unknown case with even rank r and the number of P-vertices being r - 2. In the end, a continuity problem is fully solved.& COPY; 2023 Elsevier B.V. All rights reserved.
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页数：17
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