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
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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.
@article{TIMM_2007_13_1_a9,
author = {K. V. Kostousov},
title = {Cayley graphs of the group$\mathbb Z^4$ that are limits of minimal vertex-primitive graphs of type~$HA$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {132--147},
publisher = {mathdoc},
volume = {13},
number = {1},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2007_13_1_a9/}
}
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%0 Journal Article %A K. V. Kostousov %T Cayley graphs of the group$\mathbb Z^4$ that are limits of minimal vertex-primitive graphs of type~$HA$ %J Trudy Instituta matematiki i mehaniki %D 2007 %P 132-147 %V 13 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2007_13_1_a9/ %G ru %F TIMM_2007_13_1_a9
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/