Partial graph orientations and the Tutte polynomial
نویسندگان
چکیده
منابع مشابه
Graph invariants, homomorphisms, and the Tutte polynomial
There are various ways to define the chromatic polynomial P (G; z) of a graph G. Perhaps the first that springs to mind is to define it to be the graph invariant P (G; k) with the property that when k is a positive integer P (G; k) is the number of colourings of the vertices of G with k or fewer colours such that adjacent vertices receive different colours. One then has to prove that P (G; k) i...
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A parking function of length n is a sequence (b1, b2, . . . , bn) of nonnegative integers for which there is a permutation π ∈ Sn so that 0 ≤ bπ(i) < i for all i. A well-known result about parking functions is that the polynomial Pn(q), which enumerates the complements of parking functions by the sum of their terms, is the generating function for the number of connected graphs by the number of ...
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We begin our exploration of graph polynomials and their applications with the Tutte polynomial, a renown tool for analyzing properties of graphs and networks. This two-variable graph polynomial, due to W. T. Tutte [Tut47,Tut54, Tut67], has the important universal property that essentially any multiplicative graph invariant with a deletion/contraction reduction must be an evaluation of it. These...
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The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2018
ISSN: 0196-8858
DOI: 10.1016/j.aam.2017.05.003