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

    Fingerprint

    Spatial Graph
    Complete Graph
    Congruent
    Modulo
    Theorem
    Linking number
    Knot
    Invariant
    Graph in graph theory

    Keywords

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

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    δy-exchanges and the conwaygordon theorems. / Nikkuni, Ryo; Taniyama, Kouki.

    In: Journal of Knot Theory and its Ramifications, Vol. 21, No. 7, 1250067, 06.2012.

    Research output: Contribution to journalArticle

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