A proof of the polycirculant conjecture

Details A proof of the polycirculant conjecture A proof of the polycirculant conjecture

2005-06-30

arxiv.org/abs/math/0506617v1

Mathematics

Combinatorics

6 pages

Scientific paper

This paper presents a solution of the polycirculant conjecture which states that every vertex-transitive graph G has an automorphism that permutes the vertices in cycles of the same length. This is done by identifying vertex-transitive graphs as coset graphs. For a coset graph H, an equivalence relation $\sim$ is defined on the vertices of cosets with classes as double cosets of the stabiliser and any other proper subgroup A' of a transitive group A of G. Induced left translations of elements of the subgroup A' are semi-regular since they preserve these double cosets and acts regularly on each of them. The coset graph is equivalent to G by a theorem of Sabidussi.

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