Multiparking functions, graph searching, and the Tutte polynomial
نویسندگان
چکیده
منابع مشابه
Multiparking Functions, Graph Searching, and the Tutte Polynomial
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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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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Let G be a connected graph with vertex set {0, 1, 2, . . . , n}. We allow G to have multiple edges and loops. In this paper, we give a characterization of external activity by some parameters of G-parking functions. In particular, we give the definition of the bridge vertex of a G-parking function and obtain an expression of the Tutte polynomial TG(x, y) of G in terms of G-parking functions. We...
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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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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2008
ISSN: 0196-8858
DOI: 10.1016/j.aam.2007.03.001