Geodesic
Cayley graphs of the group$\mathbb Z^4$ that are limits of minimal vertex-primitive graphs of type $HA$
Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 132-147 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the joint paper by Giudici, Li, Praeger, Seress, and Trofimov, it is proved that any graph that is a limit of vertex-primitive graphs of type $HA$ is isomorphic to a Cayley graph of the group $\mathbb Z^d$. Earlier, the author proved that for $d\le3$ the number of pairwise nonisomorphic Cayley graphs of the group $\mathbb Z^d$, which are limits of minimal vertex-primitive graphs of type $HA$, is finite (and obtained their explicit description). The present paper includes the construction of a countable family of such graphs for the case $d=4$; moreover, up to isomorphism there are only finitely many Cayley graphs of such a type outside this family. 
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K. V. Kostousov. Cayley graphs of the group$\mathbb Z^4$ that are limits of minimal vertex-primitive graphs of type $HA$. Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 132-147. http://geodesic.mathdoc.fr/item/TIMM_2007_13_1_a9/

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[2] Kostousov K. V., “Grafy Keli grupp $\mathbb Z^d$ i predely vershinno-primitivnykh grafov $HA$-tipa”, Sib. mat. zhurn., 48:3 (2007), 606–620 | MR | Zbl

[3] Kostousov K. V., “Grafy Keli gruppy $\mathbb Z^4$ i predely minimalnykh vershinno-primitivnykh grafov $HA$-tipa”, Algebra i logika, 47:2 (2008), 203–214 | MR | Zbl

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