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On Dihedralized Gyrogroups and Their Cayley Graphs

Author

Listed:
  • Rasimate Maungchang

    (School of Science, Walailak University, Nakhon Si Thammarat 80160, Thailand)

  • Teerapong Suksumran

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

The method of constructing the generalized dihedral group as a semidirect product of an abelian group and the group Z 2 of integers modulo 2 is extended to the case of gyrogroups. This leads to the study of a new class of gyrogroups, which includes generalized dihedral groups and dihedral groups as a special case. In this article, we show that any dihedralizable gyrogroup can be enlarged to a dihedralized gyrogroup. Then, we establish algebraic properties of dihedralized gyrogroups as well as combinatorial properties of their Cayley graphs.

Suggested Citation

  • Rasimate Maungchang & Teerapong Suksumran, 2022. "On Dihedralized Gyrogroups and Their Cayley Graphs," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2276-:d:851347
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    References listed on IDEAS

    as
    1. Rasimate Maungchang & Charawi Detphumi & Prathomjit Khachorncharoenkul & Teerapong Suksumran, 2022. "Hamiltonian Cycles in Cayley Graphs of Gyrogroups," Mathematics, MDPI, vol. 10(8), pages 1-11, April.
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