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Spin Models on Triangle-Free Connected Graphs

✍ Scribed by Kazumasa Nomura

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 388 KB
Volume: 67
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1996.0046

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✦ Synopsis

Spin models were introduced by V. Jones (Pac. J. Math. 137 (1989), 311 334) to construct invariants of knots and links. A spin model is defined as a pair S=(X, w) of a fine set X and a function w: X_X Ä C satisfying several axioms. Let 1=(X, E) be a connected graph with the usual metric : X_X Ä [0, 1, ..., d], where d denotes the diameter of 1. It is shown that, if 1 has no 3-cycle, and if S=(X, t b ) is a spin model for a mapping t: [0, 1, ..., d] Ä C satisfying some conditions (which hold if t is injective), then 1 is an almost bipartite distance-regular graph.

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