How to find all possible minimal edge covers over $K_6$? How to find all possible minimal edge covers over $K_6$?
$K_6$-complete graph of $6$ vertices.
On working out I found out that there would be these many cases ..
Can somebody tell me if this what I have done is right?
Or are there any more cases?

OEIS A053530 provides an exponential generating function
$$\exp(-x - x^2/2 + x\exp(x)),$$ and the count for $n=6$ is 171, which confirms that your 111 plus the missing 60 cover all cases.
