Even Dominating Sets in Complements of Powers of Cycles

n, k: n = number of vertices; k = power; so 28, 2 means
complement of C_28^2

The following do not have even dominating sets:

7, 1
7, 2
7, 3

9, 1
9, 4

11, 1
11, 2
11, 3
11, 4
11, 5

13, 1
13, 2
13, 3
13, 4
13, 5
13, 6

15, 1
15, 7

17, 1
17, 2
17, 3
17, 4
17, 5
17, 6
17, 7
17, 8

19, 1
19, 2
19, 3
19, 4
19, 5
19, 6
19, 7
19, 7
19, 9

21, 1
21, 4

If we further require that the even dominating set be connected, we exclude
any graph with N odd.