A dual graph construction for higher-rank graphs, and K-theory for finite 2-graphs

Given a k-graph Λ and an element p of Nk, we define the dual k-graph, pΛ. We show that when Λ is row-finite and has no sources, the C*-algebras C*(Λ) and C*(pΛ) coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the K-theory of C*(Λ) when Λ is finite and strongly connected and satisfies the aperiodicity condition.