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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2007, Volume 13, Number 1, Pages 132–147
(Mi timm77)
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This article is cited in 1 scientific paper (total in 1 paper)
Cayley graphs of the group$\mathbb Z^4$ that are limits of minimal vertex-primitive graphs of type $HA$
K. V. Kostousov
Abstract:
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.
Received: 15.11.2006
Citation:
K. V. Kostousov, “Cayley graphs of the group$\mathbb Z^4$ that are limits of minimal vertex-primitive graphs of type $HA$”, Группы и графы, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 1, 2007, 132–147; Proc. Steklov Inst. Math. (Suppl.), 257, suppl. 1 (2007), S118–S134
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https://www.mathnet.ru/eng/timm77 https://www.mathnet.ru/eng/timm/v13/i1/p132
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Abstract page: | 231 | Full-text PDF : | 72 | References: | 35 |
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