The extra-factorial sum for an edge e_q in WH_n sums the lengths of all (n-2)! Hamiltonian cycles containing e_q; dividing by (n-2) yields the arithmetic mean of those cycle lengths.
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Extra-factorial sum: a graph-theoretic parameter in Hamiltonian cycles of complete weighted graphs
The extra-factorial sum for an edge e_q in WH_n sums the lengths of all (n-2)! Hamiltonian cycles containing e_q; dividing by (n-2) yields the arithmetic mean of those cycle lengths.