Nonsingular acyclic matrices with full number of P-vertices

Andelić, Milica; Erić, Aleksandra; da Fonseca, C. M.

doi:10.1080/03081087.2012.661425

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Andelić, Milica

Erić, Aleksandra
da Fonseca, C. M.

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Abstract

We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In particular, we show that such trees have an even number of vertices. Both results provide answers to questions proposed by Kim and Shader. In the end, related classifications on nonsingular trees with the size of a P-set bounded are addressed.

Keywords:

graph / eigenvalues / acyclic matrices / P-vertices / P-sets

Source:
Linear & Multilinear Algebra, 2013, 61, 1, 49-57

Projects:

Center for Research and Development in Mathematics and Applications
Fundacao para a Ciencia e a Tecnologia through European Program COMPETE/FEDER
Serbian Ministry of Education and Science
Centro de Matematica da Universidade de Coimbra
Graph theory and mathematical programming with applications in chemistry and computer science (RS-174033)

DOI: 10.1080/03081087.2012.661425

ISSN: 0308-1087

WoS: 000311777000005

Scopus: 2-s2.0-84870986097

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URI

http://grafar.grf.bg.ac.rs/handle/123456789/518

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GraFar

TY  - JOUR
AU  - Andelić, Milica
AU  - Erić, Aleksandra
AU  - da Fonseca, C. M.
PY  - 2013
UR  - http://grafar.grf.bg.ac.rs/handle/123456789/518
AB  - We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In particular, we show that such trees have an even number of vertices. Both results provide answers to questions proposed by Kim and Shader. In the end, related classifications on nonsingular trees with the size of a P-set bounded are addressed.
T2  - Linear & Multilinear Algebra
T1  - Nonsingular acyclic matrices with full number of P-vertices
EP  - 57
IS  - 1
SP  - 49
VL  - 61
DO  - 10.1080/03081087.2012.661425
ER  -

@article{
author = "Andelić, Milica and Erić, Aleksandra and da Fonseca, C. M.",
year = "2013",
url = "http://grafar.grf.bg.ac.rs/handle/123456789/518",
abstract = "We classify the trees for which there is a nonsingular matrix where each vertex is a P-vertex. In particular, we show that such trees have an even number of vertices. Both results provide answers to questions proposed by Kim and Shader. In the end, related classifications on nonsingular trees with the size of a P-set bounded are addressed.",
journal = "Linear & Multilinear Algebra",
title = "Nonsingular acyclic matrices with full number of P-vertices",
pages = "57-49",
number = "1",
volume = "61",
doi = "10.1080/03081087.2012.661425"
}

Andelić, M., Erić, A.,& da Fonseca, C. M. (2013). Nonsingular acyclic matrices with full number of P-vertices.
Linear & Multilinear Algebra, 61(1), 49-57.
https://doi.org/10.1080/03081087.2012.661425

Andelić M, Erić A, da Fonseca CM. Nonsingular acyclic matrices with full number of P-vertices. Linear & Multilinear Algebra. 2013;61(1):49-57

Andelić Milica, Erić Aleksandra, da Fonseca C. M., "Nonsingular acyclic matrices with full number of P-vertices" Linear & Multilinear Algebra, 61, no. 1 (2013):49-57,
https://doi.org/10.1080/03081087.2012.661425 .