The independence number of the strong product of cycles

The independence number of the strong product of cycles is considered in this paper. We describe algorithms to search independent vertex sets in strong products of odd cycles. The algorithms enable determination of the independence number of two infinite families of graphs: C5 C7 C2k+1 and C5 C9 C2k+1. We also present exact values or improved bounds on the size of a largest independent set for several other strong products of odd cycles. Applications to the chromatic number of strong products of odd cycles and to the Shannon capacity of C7 conclude the paper.