scholarly journals Parallel edges in ribbon graphs and interpolating behavior of partial-duality polynomials

2022 ◽  
Vol 102 ◽  
pp. 103492
Author(s):  
Qiyao Chen ◽  
Yichao Chen
Keyword(s):  
Ribbon Graphs

Ribbon graphs and their invaraints derived from quantum groups

1990 ◽  
Vol 127 (1) ◽  
pp. 1-26 ◽  
Author(s):  
N. Y. Reshetikhin ◽  
V. G. Turaev
Keyword(s):  
Quantum Groups ◽  
Ribbon Graphs

Graphs, ribbon graphs, and polynomials

2021 ◽  
pp. 7-16
Author(s):  
Adrian Tanasa
Keyword(s):  
Graph Theory ◽  
Tutte Polynomial ◽  
Graph Polynomials ◽  
Ribbon Graphs

In this chapter we present some notions of graph theory that will be useful in the rest of the book. It is worth emphasizing that graph theorists and theoretical physicists adopt, unfortunately, different terminologies. We present here both terminologies, such that a sort of dictionary between these two communities can be established. We then extend the notion of graph to that of maps (or of ribbon graphs). Moreover, graph polynomials encoding these structures (the Tutte polynomial for graphs and the Bollobás–Riordan polynomial for ribbon graphs) are presented.

Partial duality for ribbon graphs, I: Distributions

2020 ◽  
Vol 86 ◽  
pp. 103084 ◽  
Author(s):  
Jonathan L. Gross ◽  
Toufik Mansour ◽  
Thomas W. Tucker
Keyword(s):  
Ribbon Graphs

scholarly journals Graphs, Links, and Duality on Surfaces

2010 ◽  
Vol 20 (2) ◽  
pp. 267-287 ◽  
Author(s):  
VYACHESLAV KRUSHKAL
Keyword(s):  
Planar Graphs ◽  
Jones Polynomial ◽  
Tutte Polynomial ◽  
Natural Duality ◽  
Polynomial Invariant ◽  
Topological Duality ◽  
Ribbon Graphs ◽  
Virtual Links ◽  
Graphs On Surfaces ◽  
Tutte Polynomials

We introduce a polynomial invariant of graphs on surfaces,PG, generalizing the classical Tutte polynomial. Topological duality on surfaces gives rise to a natural duality result forPG, analogous to the duality for the Tutte polynomial of planar graphs. This property is important from the perspective of statistical mechanics, where the Tutte polynomial is known as the partition function of the Potts model. For ribbon graphs,PGspecializes to the well-known Bollobás–Riordan polynomial, and in fact the two polynomials carry equivalent information in this context. Duality is also established for a multivariate version of the polynomialPG. We then consider a 2-variable version of the Jones polynomial for links in thickened surfaces, taking into account homological information on the surface. An analogue of Thistlethwaite's theorem is established for these generalized Jones and Tutte polynomials for virtual links.

scholarly journals FEYNMAN DIAGRAMS VIA GRAPHICAL CALCULUS

2002 ◽  
Vol 11 (07) ◽  
pp. 1095-1131 ◽  
Author(s):  
DOMENICO FIORENZA ◽  
RICCARDO MURRI
Keyword(s):  
Quantum Gravity ◽  
Asymptotic Expansions ◽  
Feynman Diagrams ◽  
Ribbon Graphs ◽  
Graphical Calculus

We use Reshetikhin-Turaev graphical calculus to define Feynman diagrams and prove that asymptotic expansions of Gaussian integrals can be written as a sum over a suitable family of graphs. We discuss how different kinds of interactions give rise to different families of graphs. In particular, we show how symmetric and cyclic interactions lead to "ordinary" and "ribbon" graphs respectively. As an example, the 't Hooft-Kontsevich model for 2D quantum gravity is treated in some detail.

scholarly journals A reduced set of moves on one-vertex ribbon graphs coming from links

2013 ◽  
Vol 142 (3) ◽  
pp. 737-752 ◽  
Author(s):  
Susan Abernathy ◽  
Cody Armond ◽  
Moshe Cohen ◽  
Oliver T. Dasbach ◽  
Hannah Manuel ◽  
...  
Keyword(s):  
Ribbon Graphs
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