\(\omega\)-periodic graphs (Q2571289)

A graph \(G\) with vertices labeled by integers is called \(\omega\)-periodic if it is a union of periodic graphs over the set of integers. It is shown that \(\omega\)-periodic graphs are amenable and the possible volume growth of \(\omega\)-periodic graphs is presented. Moreover it is shown that there are \(\omega\)-periodic graphs of (non-linear) polynomial growth as well as ones with exponential volume growth.