TY - JOUR
T1 - Arc-transitive graphs of valency twice a prime admit a semiregular automorphism
AU - Giudici, Michael
AU - Verret, Gabriel
PY - 2020
Y1 - 2020
N2 - We prove that every finite arc-transitive graph of valency twice a prime admits a nontrivial semiregular automorphism, that is, a non-identity automorphism whose cycles all have the same length. This is a special case of the Polycirculant Conjecture, which states that all finite vertex-transitive digraphs admit such automorphisms.
AB - We prove that every finite arc-transitive graph of valency twice a prime admits a nontrivial semiregular automorphism, that is, a non-identity automorphism whose cycles all have the same length. This is a special case of the Polycirculant Conjecture, which states that all finite vertex-transitive digraphs admit such automorphisms.
KW - Arc-transitive graphs
KW - Polycirculant conjecture
KW - Semiregular automorphism
UR - http://www.scopus.com/inward/record.url?scp=85090203592&partnerID=8YFLogxK
U2 - 10.26493/1855-3974.1894.37C
DO - 10.26493/1855-3974.1894.37C
M3 - Article
AN - SCOPUS:85090203592
SN - 1855-3966
VL - 18
SP - 179
EP - 186
JO - Ars Mathematica Contemporanea
JF - Ars Mathematica Contemporanea
IS - 1
ER -