Tutte polynomials and related asymptotic limiting functions for recursive families of graphs

DOI10.1016/S0196-8858(03)00077-0zbMath1041.05027arXivmath-ph/0112061MaRDI QIDQ1432997

Robert Shrock, Shu-Chiuan Chang

Publication date: 15 June 2004

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0112061

zbMATH Keywords

Potts modelTutte polynomialsflow and reliability polynomials

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Combinatorial aspects of matroids and geometric lattices (05B35) Coloring of graphs and hypergraphs (05C15)

Related Items (17)

Chromatic zeros on hierarchical lattices and equidistribution on parameter space ⋮ The Tutte polynomials of catacondensed benzenoid systems ⋮ Tutte polynomials for benzenoid systems with one branched hexagon ⋮ A general method for computing Tutte polynomials of self-similar graphs ⋮ The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs ⋮ Polynomial sequences of binomial-type arising in graph theory ⋮ Some exact results on bond percolation ⋮ On some Tutte polynomial sequences in the square lattice ⋮ The Tutte polynomial of some matroids ⋮ Asymptotic behavior of spanning forests and connected spanning subgraphs on two-dimensional lattices ⋮ Rank and Bollobás-Riordan polynomials: Coefficient measures and zeros ⋮ Tutte polynomial of the Apollonian network ⋮ Tutte polynomials of alternating polycyclic chains ⋮ Exact and Approximate Compression of Transfer Matrices for Graph Homomorphisms ⋮ Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs ⋮ Study of exponential growth constants of directed heteropolygonal Archimedean lattices ⋮ Exponential growth constants for spanning forests on Archimedean lattices: Values and comparisons of upper bounds

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