G-graph and G-gyro-graph

Autori

  • Farzaneh Gholaminezhad University of Kashan, Department of Pure Mathematics, Kashan
  • Neda Moradi University of Kashan, Department of Pure Mathematics, Kashan
  • Gholam H. Fath-Tabar University of Kashan, Department of Pure Mathematics, Kashan
  • Alain Bretto University of Caen

DOI:

https://doi.org/10.1478/AAPP.1031SA1

Parole chiave:

G-graph, G-gyro-graph, Cayley graph, Gyro-group

Abstract

In this short note, we survey several results concerning the structure of certain graphs, introduced by the fourth-named author, that can be associated to groups and gyro-groups, which are algebraic structures satisfying a twisted form of associativity. Furthermore, we include an original result, showing that the so-called G-gyro-graph associated to a gyro-group G endowed with a subset S ⊂ G is connected if and only if S is a left generating set of G. Moreover some properties and examples of both G-graphs and G-gyro-graphs are presented.

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Pubblicato

2025-02-19

Fascicolo

V. 103 N. 1 (2025)

Sezione

Survey Articles

Licenza

Creative Commons License
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