On the maximal energy among orientations of a tree
The trace norm of a digraph is the trace norm of its adjacency matrix, i.e. the sum of its singular values. Given a bipartite graph G, it is well known that the sink-source orientations have minimal trace norm among all orientations of G. In this paper, we show that the balanced orientations of G at...
- Autores:
-
Rada Rincón, Juan Pablo
Monsalve Aristazábal, Juan Daniel
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2020
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/46390
- Acceso en línea:
- https://hdl.handle.net/10495/46390
- Palabra clave:
- Teoría de grafos
Graph theory
Árboles (Teoría de grafos)
Trees (Graph theory)
Matrices (Matemáticas)
Matrices
Álgebra abstracta
Algebra, abstract
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| Summary: | The trace norm of a digraph is the trace norm of its adjacency matrix, i.e. the sum of its singular values. Given a bipartite graph G, it is well known that the sink-source orientations have minimal trace norm among all orientations of G. In this paper, we show that the balanced orientations of G attain the maximal trace norm when G is a tree with separated branching vertices, or when G is a double-star tree. We give examples of trees (with adjacent branching vertices) where non-balanced orientations have maximal trace norm. This raises the question in general: Which orientations of a tree have maximal trace norm? |
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