This paper studies some diameter-related properties of the $3$-step circulant digraphs with set of vertices $V=Z_N$ and steps $(\pm a,b)$. More precisely, it concentrates upon maximizing their order $N$ for any fixed values of their diameter $k$. In the proposed geometrical approach, each digraph is fully represented by a T-shape tile which tessellates periodically the plane. The study of these tiles leads to the optimal solutions.

Peer Reviewed