Periodic 2-graphs arising from subshifts

Higher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz– Krieger algebras. In a previous paper, we constructed 2 graphs whose path spaces are rank two subshifts of finite type, and showed that this construction yields aperiodic 2 graphs whose C algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2 graphs which we call domino graphs. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for the C algebras of domino graphs.