$\triangle Y$-exchanges and the Conway-Gordon theorems

Ryo Nikkuni; Kouki Taniyama

doi:10.1142/s0218216512500678

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arXiv · 1104.0828

$\triangle Y$-exchanges and the Conway-Gordon theorems

Ryo Nikkuni·Kouki Taniyama

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Abstract

Conway-Gordon proved that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruent to 1 modulo 2. In this paper, we give a Conway-Gordon type theorem for any graph which is obtained from the complete graph on 6 or 7 vertices by a finite sequence of $\triangle Y$-exchanges.

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Ryo Nikkuni, Kouki Taniyama. 2011-04-05. $\triangle Y$-exchanges and the Conway-Gordon theorems. https://doi.org/10.1142/s0218216512500678

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