Connected Odd Dominating Sets (CODS) in Complements of Powers of Cycles n, k: n = number of vertices; k = power; so 28, 2 means complement of C_28^2 We list only those that DO NOT have CODS: 16, 5 16, 6 24,10 Some graphs that do have CODS with the actual connected odd dominating sets listed. 28, 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 28, 2 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 28, 3 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 28, 4 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 28, 5 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 28, 6 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 28, 7 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 28, 8 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 28, 9 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 28, 10 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 28, 11 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 28, 12 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 30, 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 30,2 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 30, 3 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 30,4 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 30,5 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 30,6 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 30,7 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 30, 8 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 30,9 Many, many CODS including: 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 30, 10 Many, many CODS including: 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 30,11 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 30,12 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 30, 13 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0