Smallest independent dominating sets in Kronecker products of cycles

AbstractLet k⩾2,n=2k+1, and let m0,…,mk−1 each be a multiple of n. The graph Cm0×⋯×Cmk−1 consists of isomorphic connected components, each of which is (n−1)-regular and admits of a vertex partition into n smallest independent dominating sets. Accordingly, (independent) domination number of each connected component of this graph is equal to (1/n)th of the number of vertices in it