Properties of tiny braids and the associated commuting graph

  • Azeem Haider
  • Usman AliEmail author
  • Moin A. Ansari


In this text, we focus on a subset (called the set of tiny braids) of factors of the Garside braid and generalize some known results related to tiny braids. These generalized results, along with some combinatorics, strengthen the existing relationship between this subset and Fibonacci numbers. We also associate a commuting graph with the subset and explore its fundamental identities, including its order, diameter, girth and degree-related properties.


Fibonacci numbers Centralizer Commuting graph Positive braid Tiny braid 

Mathematics Subject Classification

11B39 05A15 05A05 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsJazan UniversityJazanSaudi Arabia
  2. 2.Centre for Advanced Studies in Pure and Applied MathematicsBahauddin Zakaria UniversityMultanPakistan
  3. 3.Institut de Mathématiques de Jussieu-Paris Rive GaucheParisFrance

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