Generalized FSSP on Two Triangular Tilings

Maignan and Yunes have already investigated solutions to the generalized firing squad synchronization problem for square tilings with both Moore and Von Neumann neighborhoods, and then shown that the same concepts could be used to handle hexagonal tilings. The communication grids for these cellular space are all very regular in a precise formal sense: they are Cayley graphs. In this paper we investigate the triangular tiling because it is very related to the hexagonal one but is not a Cayley graph. We also consider another tiling of triangles obtained by dividing every square of a square tiling into four triangles. We show that the same concepts still apply, therefore showing that the previous solutions can be extended to a broader class of spaces included in what we may call Cayley Graphs on Groupoïd.