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  • $\begingroup$ Here is the Hint which my classmates gave: Hint 1-> The number of non drawn matches is 15. Hint 2-> All graphs on 9 vertices can be found here $\endgroup$ Commented May 12 at 6:44
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    $\begingroup$ Regardless of the hint, this answer satisfies both properties. $\endgroup$
    – Dr Xorile
    Commented May 16 at 23:01