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 ℤd. Earlier, the author proved that for d ≤ 3 the number of pairwise nonisomorphic Cayley graphs of the group ℤd, 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.
Similar content being viewed by others
References
M. Giudici, C. H. Li, C. E. Praeger, A. Seress, and V. Trofimov, J. Comb. Theory. Ser. A 114, 110 (2007).
K. V. Kostousov, Sib. Mat. Zhurn., in press.
K. V. Kostousov, Algebra i Logika, in press.
Kh. Tsishang, E. Fogt, and Kh.-D. Koldevai, Surfaces and Discontinuous Groups (Nauka, Moscow, 1988).
H. Brown, H. Bulow, J. Neubuser, H. Wondratschek, and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space (John Wiley, New York, 1978).
The GAP Group. GAP-Groups, Algorithms, and Programming, Version 4.4, Aachen-St. Andrews, 2004 (http://www.gap-system.org).
E. Reingol’d, Yu. Nivergel’t, and N. Deo, Combinatorial Algorithms. Theory and Practice (Mir, Moscow, 1980).
Author information
Authors and Affiliations
Additional information
Original Russian Text © K.V. Kostousov, 2007, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2007, Vol. 13, No. 1.
Rights and permissions
About this article
Cite this article
Kostousov, K.V. Cayley graphs of the group ℤ4 that are limits of minimal vertex-primitive graphs of type HA . Proc. Steklov Inst. Math. 257 (Suppl 1), S118–S134 (2007). https://doi.org/10.1134/S0081543807050082
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0081543807050082