On transitivity and connectedness of Cayley graphs of gyrogroups

Heliyon. 2021 May 11;7(5):e07049. doi: 10.1016/j.heliyon.2021.e07049. eCollection 2021 May.

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 and applications regarding these findings are provided.

Keywords: Cayley graph; Connectedness; Gyrogroup; Transitivity; Undirected graph.