Structural and spectral properties of minimal strong digraphs

Garcia López de Lacalle, Jesús and Pozo Coronado, Luis Miguel and Marijuán López, Carlos (2016). Structural and spectral properties of minimal strong digraphs. "Electronic notes in discrete mathematics", v. 54 ; pp. 91-96. ISSN 1571-0653. https://doi.org/10.1016/j.endm.2016.09.017.

Description

Title: Structural and spectral properties of minimal strong digraphs
Author/s:
  • Garcia López de Lacalle, Jesús
  • Pozo Coronado, Luis Miguel
  • Marijuán López, Carlos
Item Type: Article
Título de Revista/Publicación: Electronic notes in discrete mathematics
Date: October 2016
ISSN: 1571-0653
Volume: 54
Subjects:
Freetext Keywords: Keywords: Minimal strong digraphs, trees, characteristic polynomial, spanning tree.
Faculty: E.T.S.I. de Sistemas Informáticos (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

EL artículo se centra en las propiedades estructurales y espectrales de los digrafos fuertemente conexos minimales, mediante la comparación de sus propiedades con las propiedades de los árboles. Este análisis incluye dos propiedades nuevas la primera da cotas para los coeficientes de los polinomios característicos de los árboles, y conjetura que esas cotas se generalizan para digrafos fuertemente conexos minimales. Como caso particular, probamos que el término independiente de tale polinomios debe ser -1, 0 o 1. La segunda establece que todo digrafo fuertemente conexo minimal puede descomponerse en un arbol generador dirigido con raíz, y un bosque de árboles con raíz inversos. En nuestra opinión, las analogías descritas entre árboles y digrafos fuertemente conexos minimales suponen un cambio significativo sobre el punto de vista acerca de estos últimos. Abstract In this article, we focus on structural and spectral properties of minimal strong digraphs (MSDs). We carry out a comparative study of properties of MSDs versus trees. This analysis includes two new properties. The first one gives bounds on the coefficients of characteristic polynomials of trees (double directed trees), and conjectures the generalization of these bounds to MSDs. As a particular case, we prove that the independent coemcient of the characteristic polynomial of a tree or an MSD must be — 1, 0 or 1. For trees, this fact means that a tree has at most one perfect matching; for MSDs, it means that an MSD has at most one covering by disjoint cycles. The property states that every MSD can be decomposed in a rooted spanning tree and a forest of reversed rooted trees, as factors. In our opinión, the analogies described suppose a significative change in the traditional point of view about this class of digraphs.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2015-65764-C3-1-PUnspecifiedUnspecifiedSingularidades, valoraciones y álgebras graduadas. Codificación

More information

Item ID: 46081
DC Identifier: http://oa.upm.es/46081/
OAI Identifier: oai:oa.upm.es:46081
DOI: 10.1016/j.endm.2016.09.017
Official URL: http://www.sciencedirect.com/science/article/pii/S1571065316301111
Deposited by: Memoria Investigacion
Deposited on: 29 May 2017 18:51
Last Modified: 20 Mar 2019 18:37
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