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arXiv · 2008.03267

On transitivity and connectedness of Cayley graphs of gyrogroups

Rasimate Maungchang·Prathomjit Khachorncharoenkul·Kiattisak Prathom·Teerapong Suksumran
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Abstract

In this work, we explore edge direction, transitivity, and connectedness of Cayley graphs of gyrogroups. More specifically, we find conditions for a Cayley graph of a gyrogroup to be undirected, transitive, and connected. We also show a relationship between the cosets of a certain type of subgyrogroups and the connected components of Cayley graphs. Some examples regarding these findings are provided.

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Rasimate Maungchang, Prathomjit Khachorncharoenkul, Kiattisak Prathom, Teerapong Suksumran. 2020-08-07. On transitivity and connectedness of Cayley graphs of gyrogroups. https://doi.org/10.1016/j.heliyon.2021.e07049

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