✦ LIBER ✦

Knot graphs

✍ Scribed by Noble, S. D.; Welsh, D. J. A.

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 148 KB
Volume: 34
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r

No coin nor oath required. For personal study only.

✦ Synopsis

We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph that is reducible by some finite sequence of these moves, to a graph with no edges, is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of the intersection of the cycle and cocycle spaces is an effective numerical invariant of these classes.

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