Odd automorphisms in vertex-transitive graphs

Ademir Hujdurović, Klavdija Kutnar, Dragan Marušič


An automorphism of a graph is said to be even/odd if it acts on the set of vertices as an even/odd permutation. In this article we pose the problem of determining which vertex-transitive graphs admit odd automorphisms. Partial results for certain classes of vertex-transitive graphs, in particular for Cayley graphs, are given. As a consequence, a characterization of arc-transitive circulants without odd automorphisms is obtained.


Graph, vertex-transitive, automorphism group, even permutation, odd permutation

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DOI: https://doi.org/10.26493/1855-3974.1046.980

ISSN: 1855-3974

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