Semiregular automorphisms in vertex-transitive graphs of order \(3p^2\)
The electronic journal of combinatorics, Tome 25 (2018) no. 2
It has been conjectured that automorphism groups of vertex-transitive (di)graphs, and more generally $2$-closures of transitive permutation groups, must necessarily possess a fixed-point-free element of prime order, and thus a non-identity element with all orbits of the same length, in other words, a semiregular element. It is the purpose of this paper to prove that vertex-transitive graphs of order $3p^2$, where $p$ is a prime, contain semiregular automorphisms.
DOI :
10.37236/7499
Classification :
20B25, 05C25
Mots-clés : vertex-transitive graph, semiregular automorphism, polycirculant conjecture
Mots-clés : vertex-transitive graph, semiregular automorphism, polycirculant conjecture
Affiliations des auteurs :
Dragan Marušič 1
@article{10_37236_7499,
author = {Dragan Maru\v{s}i\v{c}},
title = {Semiregular automorphisms in vertex-transitive graphs of order \(3p^2\)},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {2},
doi = {10.37236/7499},
zbl = {1458.20003},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7499/}
}
Dragan Marušič. Semiregular automorphisms in vertex-transitive graphs of order \(3p^2\). The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7499
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