Abstract
Let be a connected locally finite vertex-symmetric graph, the number of vertices of at a distance not more than from some fixed vertex. The equivalence of the following assertions is proved:(a) is bounded above by a polynomial.(b) There is an imprimitivity system with finite blocks of on the set of vertices of such that is finitely generated nilpotent-by-finite and the stabilizer of a vertex of in is finite.Thus, in a certain sense, a description is obtained of the connected locally finite vertex-symmetric graphs with polynomial growth.Bibliography. 8 titles.
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