A restricted permutation of a locally finite directed graph $ G = (V, E) $ is a vertex permutation $ \pi: V\to V $ for which $ (v, \pi(v))\in E $, for any vertex $ v\in V $. The set of such permutations, denoted by $ \Omega(G) $, with a group action induced from a subset of graph isomorphisms form a topological dynamical system. We focus on the particular case presented by Schmidt and Strasser [
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(a) The two-dimensional honeycomb lattice. (b) The fundamental domain
(a) Paths configuration corresponding to an elements in
The graphs corresponding to
The graph
The quotient of
A correspondence between a function in
(a) The
The correspondence between a restricted permutation of the honeycomb lattice, perfect matchings and permutations of
The corresponding graph for
A locally admissible pattern which is not globally admissible where the restricting set is
The extension of