Finite s-Arc Transitive Cayley graphs and Flag-Transitive Projective Planes

    Research output: Contribution to journalArticle

    24 Citations (Scopus)

    Abstract

    In this paper, a characterisation is given of finite s-arc transitive Cayley graphs with s≥2. In particular, it is shown that, for any given integer k with k≥3 and k≠7, there exists a finite set (maybe empty) of s-transitive Cayley graphs with s ε{3,4,5,7} such that all s-transitive Cayley graphs of valency k are their normal covers. This indicates that s-arc transitive Cayley graphs with s≥3 are very rare. However, it is proved that there exist 4-arc transitive Cayley graphs for each admissible valency (a prime power plus one). It is then shown that the existence of a flag-transitive non-Desarguesian projective plane is equivalent to the existence of a very special arc transitive normal Cayley graph of a dihedral group.
    Original languageEnglish
    Pages (from-to)31-41
    JournalProceedings of the American Mathematical Society
    Volume133
    Issue number1
    DOIs
    Publication statusPublished - 2005

    Fingerprint Dive into the research topics of 'Finite s-Arc Transitive Cayley graphs and Flag-Transitive Projective Planes'. Together they form a unique fingerprint.

    Cite this