Cayley graphs of groups $\mathbb Z^4$, $\mathbb Z^5$ and $\mathbb Z^6$ which are limit graphs for the finite graphs of minimal valency for vertex-primitive groups of automorphisms
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 88-150
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Infinite connected graph $\Gamma$ is called a limit graph for the set $X$ of finite vertex-primitive graphs, if each ball of $\Gamma$ is isomorphic to a ball of some graph in $X$. A finite graph $\Gamma$ is called a graph of minimal degree for a vertex-primitive group $G\le\operatorname{Aut}(\Gamma)$, if the condition $\deg(\Gamma)\le\deg(\Delta)$ is hold for any graph $\Delta$ such that $V(\Delta)=V(\Gamma)$ and
$G\le\operatorname{Aut}(\Delta)$. It is obtained the description of Cayley graphs of groups $\mathbb Z^4$, $\mathbb Z^5$ and $\mathbb Z^6$ which are limit graphs for the finite graphs of minimal degree for vertex-primitive groups of automorphisms.
@article{SEMR_2008_5_a10,
author = {K. V. Kostousov},
title = {Cayley graphs of groups $\mathbb Z^4$, $\mathbb Z^5$ and $\mathbb Z^6$ which are limit graphs for the finite graphs of minimal valency for vertex-primitive groups of automorphisms},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {88--150},
publisher = {mathdoc},
volume = {5},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a10/}
}
TY - JOUR AU - K. V. Kostousov TI - Cayley graphs of groups $\mathbb Z^4$, $\mathbb Z^5$ and $\mathbb Z^6$ which are limit graphs for the finite graphs of minimal valency for vertex-primitive groups of automorphisms JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2008 SP - 88 EP - 150 VL - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2008_5_a10/ LA - ru ID - SEMR_2008_5_a10 ER -
%0 Journal Article %A K. V. Kostousov %T Cayley graphs of groups $\mathbb Z^4$, $\mathbb Z^5$ and $\mathbb Z^6$ which are limit graphs for the finite graphs of minimal valency for vertex-primitive groups of automorphisms %J Sibirskie èlektronnye matematičeskie izvestiâ %D 2008 %P 88-150 %V 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/SEMR_2008_5_a10/ %G ru %F SEMR_2008_5_a10
K. V. Kostousov. Cayley graphs of groups $\mathbb Z^4$, $\mathbb Z^5$ and $\mathbb Z^6$ which are limit graphs for the finite graphs of minimal valency for vertex-primitive groups of automorphisms. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 88-150. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a10/