Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M25, 05C99, 57M15

Retrieve articles in all journals with MSC: 57M25, 05C99, 57M15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0930077-6
PII: S 0002-9947(1989)0930077-6
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