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?
2026-05-17 06:05:39.1778997939
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How to find all possible minimal edge covers over $K_6$?
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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.
What about $a$ conected to $b,c,d$ and $e-f$ that is $4$ edges.
So you have ${6\choose 2}\cdot {4\choose 1}$ more minimal $4$-edges cover.