On transitivity and connectedness of Cayley graphs of gyrogroups
Rasimate Maungchang, Prathomjit Khachorncharoenkul, Kiattisak Prathom, and Teerapong Suksumran
TL;DR
This paper investigates the properties of Cayley graphs of gyrogroups, focusing on conditions for undirectedness, transitivity, and connectedness, and explores how subgyrogroup cosets relate to graph components.
Contribution
It provides new conditions for Cayley graphs of gyrogroups to be undirected, transitive, and connected, and links subgyrogroup cosets to graph connected components.
Findings
Conditions for Cayley graphs to be undirected, transitive, and connected
Relationship between subgyrogroup cosets and connected components
Examples illustrating these properties
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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