Spanning trees on graphs and lattices inddimensions
نویسندگان
چکیده
منابع مشابه
Spanning trees on graphs and lattices in d dimensions
The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees NST and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A general formulation is presented for the enumeration of spanning trees on lattices in d 2 dimensions, and is applied to the hypercubic, body-centred cubic, face-ce...
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For a lattice Λ with n vertices and dimension d equal or higher than two, the number of spanning trees N ST (Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant z Λ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also gi...
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A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
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In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
متن کاملOn Universal Graphs for Spanning Trees
Introduction A number of papers [1,2,3,4,6] recently have been concerned with the following question. What is the minimum number s{n) of edges a graph G on n vertices can have so that any tree on n vertices is isomorphic to some spanning tree of G? We call such a graph universal for spanning trees. Since Kn, the complete graph on n vertices (see [5] for terminology), has the required property, ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2000
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/33/21/303