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On the Degree Distribution of Haros Graphs

Author

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  • Jorge Calero-Sanz

    (ETSI Aeronáutica y del Espacio (ETSIAE), Universidad Politécnica de Madrid, 28040 Madrid, Spain
    Department of Signal Theory and Communications, Telematics and Computing Systems, Rey Juan Carlos University, 28942 Fuenlabrada, Spain)

Abstract

Haros graphs are a graph-theoretical representation of real numbers in the unit interval. The degree distribution of the Haros graphs provides information regarding the topological structure and the associated real number. This article provides a comprehensive demonstration of a conjecture concerning the analytical formulation of the degree distribution. Specifically, a theorem outlines the relationship between Haros graphs, the corresponding continued fraction of its associated real number, and the subsequent symbolic paths in the Farey binary tree. Moreover, an expression that is continuous and piecewise linear in subintervals defined by Farey fractions can be derived from an additional conclusion for the degree distribution of Haros graphs.

Suggested Citation

  • Jorge Calero-Sanz, 2022. "On the Degree Distribution of Haros Graphs," Mathematics, MDPI, vol. 11(1), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:92-:d:1015117
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    References listed on IDEAS

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    1. Bartolo Luque & Lucas Lacasa & Fernando J Ballesteros & Alberto Robledo, 2011. "Feigenbaum Graphs: A Complex Network Perspective of Chaos," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-8, September.
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