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
SN - 0218-2165
VL - 21
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 7
M1 - 1250067
ER -