A graph $\Gamma$ is edge-transitive ($s$-arc-transitive, respectively) if its full automorphism group $\rm Aut\,(\Gamma)$ acts transitively on the set of edges (the set of $s$-arcs in $\Gamma$ for an integer $s\geq 0$, respectively). A $1$-arc-transitive graph is called an arc-transitive graph or a symmetric graph. In this paper, we construct cubic symmetric bi-Cayley graphs over some groups of order $p^4$, where $p\geq 7$ is a prime. Using these constructions, we classify the connected cubic edge-transitive graphs of order $2p^4$ for each prime $p$ and we also show that all these graphs are symmetric.
@article{10_37236_13675,
author = {Xue Wang and Sejeong Bang and Jin-Xin Zhou},
title = {Cubic edge-transitive graphs of order \(2p^4\)},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/13675},
zbl = {8097679},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13675/}
}
TY - JOUR
AU - Xue Wang
AU - Sejeong Bang
AU - Jin-Xin Zhou
TI - Cubic edge-transitive graphs of order \(2p^4\)
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/13675/
DO - 10.37236/13675
ID - 10_37236_13675
ER -
%0 Journal Article
%A Xue Wang
%A Sejeong Bang
%A Jin-Xin Zhou
%T Cubic edge-transitive graphs of order \(2p^4\)
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/13675/
%R 10.37236/13675
%F 10_37236_13675
Xue Wang; Sejeong Bang; Jin-Xin Zhou. Cubic edge-transitive graphs of order \(2p^4\). The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13675
