Using a simple but rather general method of constructing Cayley graphs with trivial vertex stabilizers, we give an example of an infinite locally finite Cayley graph (and, hence, an example of an infinite connected locally finite vertex-symmetric unimodular graph) which is isolated in the space of connected locally finite vertex-symmetric graphs. We also give examples of Cayley graphs which are not isolated in this space but are isolated from the set of connected vertex-symmetric finite graphs.
Keywords: connected locally finite vertex-symmetric graph, Cayley graph, convergence of graphs
Received September 19, 2019
Revised October 15 2019
Accepted October 21, 2019
Trofimov Vladimir Ivanovich, Dr. Phys.-Math. Sci., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620002 Russia, e-mail: trofimov@imm.uran.ru
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Cite this article as: V.I.Trofimov. On limits of vertex-symmetric graphs and their automorphisms, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 4, pp. 226–234.
