A family of Cayley graphs on the hexavalent grid Original Research Article

The paper is concerned with a family of tori (i.e. arrowhead and diamond) which we define on the triangular (or “hexavalent”) grid. Their related interconnection networks have several important advantages. They have a bounded valence and the highest allowed valence for a 2D regular grid. They are good hosts for embedding the normal grid. As hierarchical Cayley graphs, they allow recursive constructions and divide-and-conquer schemes for information dissemination and will provide a suitable framework to set up efficient strategies for broadcasting.