Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On invariants of graphs with applications to knot theory

Author: Kunio Murasugi
Journal: Trans. Amer. Math. Soc. 314 (1989), 1-49
MSC: Primary 57M25; Secondary 05C99, 57M15
MathSciNet review: 930077
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Abstract: To each weighted graph $ \Gamma $, two invariants, a polynomial $ {P_\Gamma }(x,y,z)$ and the signature $ \sigma (\Gamma)$, are defined. The various partial degress of $ {P_\Gamma }(x,y,z)$ and $ \sigma (\Gamma)$ are expressed in terms of maximal spanning graphs of $ \Gamma $. Furthermore, one unexpected property of Tutte's dichromate is proved. These results are applied to knots or links in $ {S^3}$.

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Keywords: Weighted graph, polynomial of a graph, signature, Tutte's dichromate knot, link, Jones polynomial, chromatic degree, maximal spanning subgraph, alternating knot
Article copyright: © Copyright 1989 American Mathematical Society