Results 41 to 50 of about 3,648 (134)

Tutte polynomials for directed graphs

Journal of Combinatorial Theory, Series B, 2020
The Tutte polynomial is a fundamental invariant of graphs. In this article, we define and study a generalization of the Tutte polynomial for directed graphs, that we name B-polynomial. The B-polynomial has three variables, but when specialized to the case of graphs (that is, digraphs where arcs come in pairs with opposite directions), one of the ...
Awan, Jordan, Bernardi, Olivier
openaire   +4 more sources

The Arithmetic Tutte polynomial of two matrices associated to Trees

Special Matrices, 2018
Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors
Bapat R. B., Sivasubramanian Sivaramakrishnan   +1 more
doaj   +1 more source

The equivalence of two graph polynomials and a symmetric function [PDF]

, 2009
The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial due to Stanley are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the coefficients of any ...
Merino, C, Noble, SD
core   +1 more source

Tutte Polynomial of Multi-Bridge Graphs [PDF]

Computer Science Journal of Moldova, 2013
In this paper, using a well-known recursion for computing the Tutte polynomial of any graph, we found explicit formulae for the Tutte polynomials of any multi-bridge graph and some $2-$tree graphs.
Julian A. Allagan
doaj  

Zeros of Jones Polynomials for Families of Knots and Links

, 2001
We calculate Jones polynomials $V_L(t)$ for several families of alternating knots and links by computing the Tutte polynomials $T(G,x,y)$ for the associated graphs $G$ and then obtaining $V_L(t)$ as a special case of the Tutte polynomial.
Abe, Baxter, Beraha, Beraha, Biggs, Biggs, Biggs, Bollobás, Burde, Chang, Chang, Chang, Chang, Chang, Chang, Chen, Feldmann, Feldmann, Feldmann, Fortuin, Itzykson, Jones, Jones, Jones, Kasteleyn, Kauffman, Lee, Lickorish, Marchesini, Martin, Martin, Matveev, Matveev, Matveev, Matveev, Matveev, Ono, R. Shrock, Read, Roc̆ek, Roc̆ek, Rolfsen, S.-C. Chang, Salas, Shrock, Shrock, Shrock, Shrock, Shrock, Shrock, Shrock, Shrock, Shrock, Sokal, Stephenson, Tutte, Tutte, Tutte, van Saarloos, Welsh, Wu, Wu, Wu, Yang, Yang, Yang   +65 more
core   +3 more sources

Relations between M\"obius and coboundary polynomial [PDF]

, 2012
It is known that, in general, the coboundary polynomial and the M\"obius polynomial of a matroid do not determine each other. Less is known about more specific cases.
A. Faldum, C. Greene, D.J.A. Welsh, F.J. MacWilliams, H. Crapo, I.M. Duursma, I.M. Duursma, I.M. Duursma, J.G. Oxley, M. Aigner, M.A. Boer de, N. White, R.P.M.J. Jurrius, Relinde Jurrius, T. Kløve, T. Zaslavsky   +15 more
core   +3 more sources

Bipartition Polynomials, the Ising Model, and Domination in Graphs

Discussiones Mathematicae Graph Theory, 2015
This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph.
Dod Markus, Kotek Tomer, Preen James, Tittmann Peter   +3 more
doaj   +1 more source

The Interlace Polynomial

, 2016
In this paper, we survey results regarding the interlace polynomial of a graph, connections to such graph polynomials as the Martin and Tutte polynomials, and generalizations to the realms of isotropic systems and delta-matroids.Comment: 18 pages, 5 ...
Morse, Ada
core   +1 more source

Orienting Transversals and Transition Polynomials of Multimatroids

, 2017
Multimatroids generalize matroids, delta-matroids, and isotropic systems, and transition polynomials of multimatroids subsume various polynomials for these latter combinatorial structures, such as the interlace polynomial and the Tutte-Martin polynomial.
Brijder, Robert
core   +1 more source

On the rooted Tutte polynomial [PDF]

, 1998
The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors.
King, C., Lu, W. T., Wu, F. Y.
core   +3 more sources