Abstract:
A primitive permutation group is called a group of HA-type, if it contains regular abelian normal subgroup. A finite connected graph $\Gamma$ is called a minimal vertex-primitive graph of HA-type, if there exists a vertex-primitive group $G$ of automorphisms of $\Gamma$ of HA-type, such that $\Gamma$ has a minimal degree among all connected graphs $\Delta$, with $V(\Delta)=V(\Gamma)$ and $G\leq \mathrm{Aut}\,(\Delta)$. For the class of minimal vertex-primitive graphs of HA-type we find all limit graphs of degree less than 24 (it is shown that there are 23 such graphs). In the previous paper the author proved that there are infinitely many such limit graphs of degree 24.
Fulltext:
PDF file (669 kB)