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This research was funded by Universidad Politecnica Salesiana and supported by Math Innovation Group and Departamento de MATIC.

Analysis of institutional authors

Pozo-Coronado, Luis MAuthor

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December 24, 2024
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Cyclic Structure, Vertex Degree and Number of Linear Vertices in Minimal Strong Digraphs

Publicated to:Mathematics. 12 (23): 3657- - 2024-12-01 12(23), DOI: 10.3390/math12233657

Authors: Arcos-Argudo, M; Lacalle, J; Pozo-Coronado, LM

Affiliations

Univ Politecn Madrid, Dept MATIC, ETSI Sistemas Informat, Madrid 28031, Spain - Author
Univ Politecn Salesiana, Math Innovat Grp, Cuenca 010102, Ecuador - Author

Abstract

Minimal Strong Digraphs (MSDs) can be regarded as a generalization of the concept of tree to directed graphs. Their cyclic structure and some spectral properties have been studied in several articles. In this work, we further study some properties of MSDs that have to do with bounding the length of the longest cycle (regarding the number of linear vertices, or the maximal in- or outdegree of vertices); studying whatever consequences from the spectral point of view; and giving some insight about the circumstances in which an efficient algorithm to find the longest cycle contained in an MSD can be formulated. Among other properties, we show that the number of linear vertices contained in an MSD is greater than or equal to the maximal (respectively minimal) in- or outdegree of any vertex of the MSD and that the maximal length of a cycle contained in an MSD is lesser than or equal to 2n-m where n,m are the order and the size of the MSD, respectively; we find a bound for the coefficients of the characteristic polynomial of an MSD, and finally, we prove that computing the longest cycle contained in an MSD is an NP-hard problem.

Keywords

Characteristic polynomialExternal chainLinear vertexMaximum length directed cyclesMinimal strong digraphsNp-hard proble

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 29/483, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics. Notably, the journal is positioned above the 90th percentile.

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-23:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 1.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 1.
  • The number of mentions on the social network X (formerly Twitter): 1 (Altmetric).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/87277/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 38
  • Downloads: 28

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Ecuador.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Arcos-Argudo, Miguel) and Last Author (POZO CORONADO, LUIS MIGUEL).

the author responsible for correspondence tasks has been Arcos-Argudo, Miguel.