A graph is said to be a bi-Cayley graph over a group $H$ if it admits $H$ as a group of automorphisms acting semiregularly on its vertices with two orbits. For a prime $p$, we call a bi-Cayley graph over a metacyclic $p$-group a bi-$p$-metacirculant. In this paper, the automorphism group of a connected cubic edge-transitive bi-$p$-metacirculant is characterized for an odd prime $p$, and the result reveals that a connected cubic edge-transitive bi-$p$-metacirculant exists only when $p=3$. Using this, a classification is given of connected cubic edge-transitive bi-Cayley graphs over an inner-abelian metacyclic $3$-group. As a result, we construct the first known infinite family of cubic semisymmetric graphs of order twice a $3$-power.
@article{10_37236_6417,
author = {Yan-Li Qin and Jin-Xin Zhou},
title = {Cubic edge-transitive bi-\(p\)-metacirculants},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/6417},
zbl = {1395.05080},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6417/}
}
TY - JOUR
AU - Yan-Li Qin
AU - Jin-Xin Zhou
TI - Cubic edge-transitive bi-\(p\)-metacirculants
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/6417/
DO - 10.37236/6417
ID - 10_37236_6417
ER -
