\triangle Y-exchanges and the Conway-Gordon theorems

2011/04/30 by Ryo Nikkuni, Kouki Taniyama · 1 citation
Mathematics · #math.GT #msc:57M15 #msc:57M25

paper · pdf · doi:10.1142/s0218216512500678

published as J. Knot Theory Ramifications 21 (2012), 1250067 · 12 pages, 5 figures

arxiv created 2011/09/23 · arxiv updated 2020/05/19

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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• ON CONWAY–GORDON TYPE THEOREMS FOR GRAPHS IN THE PETERSEN FAMILY

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