δy-exchanges and the conwaygordon theorems

Ryo Nikkuni, Kouki Taniyama

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number1250067
JournalJournal of Knot Theory and its Ramifications
Volume21
Issue number7
DOIs
Publication statusPublished - 2012 Jun 1

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Keywords

  • Intrinsic knottedness
  • Intrinsic linkedness
  • Spatial graph
  • δY-exchange

ASJC Scopus subject areas

  • Algebra and Number Theory

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