Nonsingular acyclic matrices with full number of P-vertices
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-setsSource:
Linear & Multilinear Algebra, 2013, 61, 1, 49-57Funding / 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-MESTD-Basic Research (BR or ON)-174033)
DOI: 10.1080/03081087.2012.661425
ISSN: 0308-1087