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Structural characterization of Cayley graphs

2016/09/27 by Didier Caucal, Caucal, Didier
Computer Science · Materials Science · #05C25 #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Supramolecular Self-Assembly in Materials

paper · pdf · doi:10.48550/arxiv.1609.08272

openalex publication_date 2016/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle language, or just the same elementary cycle language. Under the assumption of the axiom of choice, we characterize the Cayley graphs for all group subsets as the deterministic, co-deterministic, vertex-transitive simple graphs.

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