Speaker
Istvan Kovacs
Description
A non-trivial automorphism $g$ of a graph $\Gamma$ is called semiregular
if the only power $g^i$ fixing a vertex is the identity mapping,
and it is called quasi-semiregular if it fixes one
vertex and the only power $g^i$ fixing another vertex is the identity mapping. In this paper, we prove that $K_4,$ the Petersen graph and the Coxeter graph are the only connected cubic arc-transitive graphs admitting a quasi-semiregular automorphism, and $K_5$ is the only connected tetravalent $2$-arc-transitive graph admitting a quasi-semiregular automorphism. It will also be shown that every
connected tetravalent $G$-arc-transitive graph, where $G$ is a solvable group containing a quasi-semiregular automorphism, is a normal Cayley graph of an abelian group of odd order.
Primary authors
Ademir Hujdurović
Dragan Marušič
Istvan Kovacs
Klavdija Kutnar
Yan-Quan Feng
(Beijing Jiaotong University)
