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oai:uvadoc.uva.es:10324/407342021-06-24T07:41:26Zcom_10324_32197com_10324_952com_10324_894col_10324_32199

Structural and spectral properties of minimal strong digraphs Marijuán López, Carlos García López, Jesús Pozo Coronado, Luis Miguel 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. 2020-04-13T13:11:53Z 2020-04-13T13:11:53Z 2020-04-13T13:11:53Z 2016 info:eu-repo/semantics/article Electronic Notes in Discrete Mathematics, 2016, vol. 54. p. 91-96 1571-0653 http://uvadoc.uva.es/handle/10324/40734 10.1016/j.endm.2016.09.017 eng https://www.sciencedirect.com/science/article/abs/pii/S1571065316301111 info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2016 Elsevier Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier