Tutte polynomial of a small-world Farey graph
1 Department of Mathematics, Hunan First Normal University - Changsha, Hunan 410205, China
2 Department of Mathematics, Hunan Normal University - Changsha, Hunan 410081, China
Received: 18 July 2013
Accepted: 28 October 2013
In this paper, we find recursive formulas for the Tutte polynomials of a family of small-world Farey graphs, which are modular, and has an exponential degree hierarchy. As applications of the recursive formula, the exact expressions for the chromatic polynomial and the reliability polynomial of Fare graphs are derived and the number of connected spanning subgraphs is also obtained.
PACS: 89.75.Hc – Networks and genealogical trees / 02.10.Ox – Combinatorics; graph theory / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EPLA, 2013