Constructing infinite one-regular graphs
A graph \(X\) is said to be one-regular if the automorphism group of \(X\) acts regularly on the set of arcs of \(X\). The authors consider infinite one-regular graphs. Starting with an infinite family of finite one-regular graphs of valency 4, for each member of this family an infinite one-regular graph is constructed. These graphs are Cayley graphs of almost abelian groups and represent a subclass of graphs with polynomial growth.
scientific article; zbMATH DE number 1417661
scientific article