New families of multiplicative circulant networks

For circulant networks, the problem of the maximal attainable number of nodes under given degree and diameter of their graphs is considered. A research of multiplicative circulant networks with generators in the form of $(1,t,t^2,\dots, t^{k-1})$ for odd $t\ge5$ is presented. On the base of this research, two new families of multiplicative circulant networks of orders $n=(t+1)(1+t+\ldots+t^{k-1})/2+t^{k-1}$ for odd dimensions $k\ge3$ and diameters $d\equiv0\bmod k$ and even dimensions $k\ge4$ and diameters $d\equiv0\bmod k$ and $d\equiv0\bmod k/2$ are constructed. The orders of these graphs are larger than orders of graphs of all known families of multiplicative circulant networks under the same dimensions and diameters.