Nonsingular acyclic matrices with full number of P-vertices
Apstrakt
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.
Ključne reči:
graph / eigenvalues / acyclic matrices / P-vertices / P-setsIzvor:
Linear & Multilinear Algebra, 2013, 61, 1, 49-57Finansiranje / projekti:
- 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
- Teorija grafova i matematičko programiranje sa primenama u hemiji i računarstvu (RS-MESTD-Basic Research (BR or ON)-174033)
DOI: 10.1080/03081087.2012.661425
ISSN: 0308-1087
WoS: 000311777000005
Scopus: 2-s2.0-84870986097
Kolekcije
Institucija/grupa
GraFarTY - JOUR AU - Andelić, Milica AU - Erić, Aleksandra AU - da Fonseca, C. M. PY - 2013 UR - https://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", 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. in 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. in Linear & Multilinear Algebra. 2013;61(1):49-57. doi:10.1080/03081087.2012.661425 .
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 . .