Mating graph problem

[Vladeta Jovovic]

Seqfans,


Is it easy to find a "natural" bijection between classes P(n-1) and Q(n), n>0, where


P(n)  is the class of labeled mating graphs on n nodes, allowing loops and without isolated nodes

and

Q(n)   is the class of labeled mating graphs on n nodes?


Graph G is mating graph iff its adjacency matrix has no pair of equal rows, see A006024.


Regards,
Vladeta


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