TY - JOUR

T1 - δy-exchanges and the conwaygordon theorems

AU - Nikkuni, Ryo

AU - Taniyama, Kouki

N1 - Funding Information:
The first author was partially supported by Grant-in-Aid for Young Scientists (B) (No. 21740046), Japan Society for the Promotion of Science. The second author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 21540099), Japan Society for the Promotion of Science.

PY - 2012/6

Y1 - 2012/6

N2 - ConwayGordon proved that for every spatial complete graph on six 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 seven 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 ConwayGordon type theorem for any graph which is obtained from the complete graph on six or seven vertices by a finite sequence of △Y-exchanges.

AB - ConwayGordon proved that for every spatial complete graph on six 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 seven 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 ConwayGordon type theorem for any graph which is obtained from the complete graph on six or seven vertices by a finite sequence of △Y-exchanges.

KW - Intrinsic knottedness

KW - Intrinsic linkedness

KW - Spatial graph

KW - δY-exchange

UR - http://www.scopus.com/inward/record.url?scp=84859406231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859406231&partnerID=8YFLogxK

U2 - 10.1142/S0218216512500678

DO - 10.1142/S0218216512500678

M3 - Article

AN - SCOPUS:84859406231

VL - 21

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 7

M1 - 1250067

ER -