Geodesic
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 
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/
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     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},
     year = {2008},
     volume = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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