A family of efficient six-regular circulants representable as a Kronecker product
Broere and Hattingh proved that the Kronecker product of two circulants whose orders are co-prime is a circulant itself. This paper builds on this result to construct a family of efficient three-colorable, six-regular circulants representable as the Kronecker product of a Mbius ladder and an odd cycle. The order of each graph is equal to 4d2?2d?2 4 d 2 ? 2 d ? 2 where d d denotes the diameter and d?3,5 d ? 3 , 5 (mod 6). Additional results include (a) distance-wise vertex distribution of the circulant leading to its average distance that is about two-thirds of the diameter, (b) routing via shortest paths, and (c) an embedding of the circulant on a torus with a half twist. In terms of the orderdiameter ratio and odd girth, the circulants in this paper surpass the well-known triple-loop networks having diameter d d and order 3d2+3d+1 3 d 2 + 3 d + 1 .
six-regular circulants kronecker product mbius ladder routing embedding twisted torus network topology graphs and networks