A graph is vertex-transitive if its automorphism group acts transitively on its vertices. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, the cubic vertex-transitive non-Cayley graphs of order $8p$ are classified for each prime $p$. It follows from this classification that there are two sporadic and two infinite families of such graphs, of which the sporadic ones have order $56$, one infinite family exists for every prime $p>3$ and the other family exists if and only if $p\equiv 1\mod 4$. For each family there is a unique graph for a given order.
@article{10_37236_2087,
author = {Jin-Xin Zhou and Yan-Quan Feng},
title = {Cubic vertex-transitive {non-Cayley} graphs of order \(8p\)},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {1},
doi = {10.37236/2087},
zbl = {1243.05111},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2087/}
}
TY - JOUR
AU - Jin-Xin Zhou
AU - Yan-Quan Feng
TI - Cubic vertex-transitive non-Cayley graphs of order \(8p\)
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2087/
DO - 10.37236/2087
ID - 10_37236_2087
ER -
%0 Journal Article
%A Jin-Xin Zhou
%A Yan-Quan Feng
%T Cubic vertex-transitive non-Cayley graphs of order \(8p\)
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2087/
%R 10.37236/2087
%F 10_37236_2087
Jin-Xin Zhou; Yan-Quan Feng. Cubic vertex-transitive non-Cayley graphs of order \(8p\). The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/2087
