Nonsingular acyclic matrices with full number of P-vertices
Апстракт
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.
Кључне речи:
graph / eigenvalues / acyclic matrices / P-vertices / P-setsИзвор:
Linear & Multilinear Algebra, 2013, 61, 1, 49-57Финансирање / пројекти:
- 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
- Теорија графова и математичко програмирање са применама у хемији и рачунарству (RS-174033)
DOI: 10.1080/03081087.2012.661425
ISSN: 0308-1087