Geodesic
Limit graphs of degree less than 24 for minimal vertex-primitive graphs of HA-type
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 130-149

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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.
Keywords: vertex-primitive graph, limit graph, Cayley graph, free abelian group. 
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     author = {K. V. Kostousov},
     title = {Limit graphs of degree less than 24 for minimal vertex-primitive graphs of {HA-type}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {130--149},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a4/}
}
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K. V. Kostousov. Limit graphs of degree less than 24 for minimal vertex-primitive graphs of HA-type. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 130-149. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a4/