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.
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
UR - conv_1597
ER -
@article{
author = "Andelić, Milica and Erić, Aleksandra and da Fonseca, C. M.",
year = "2013",
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",
url = "conv_1597"
}
Andelić, M., Erić, A.,& da Fonseca, C. M.. (2013). Nonsingular acyclic matrices with full number of P-vertices. in Linear & Multilinear Algebra, 61(1), 49-57.
https://doi.org/10.1080/03081087.2012.661425
conv_1597
Andelić M, Erić A, da Fonseca CM. Nonsingular acyclic matrices with full number of P-vertices. in Linear & Multilinear Algebra. 2013;61(1):49-57.
doi:10.1080/03081087.2012.661425
conv_1597 .
Andelić, Milica, Erić, Aleksandra, da Fonseca, C. M., "Nonsingular acyclic matrices with full number of P-vertices" in Linear & Multilinear Algebra, 61, no. 1 (2013):49-57,
https://doi.org/10.1080/03081087.2012.661425 .,
conv_1597 .
