Tutte polynomial of a small-world Farey graph

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...

Generalized Farey Tree Network with Small-World

Generalized Farey tree network (GFTN) model with small-world is proposed, and the topological characteristics are studied by both theoretical analysis and numerical simulations, which are in good accordance with each other. Analytical results show that the degree distribution of the GFTN is exponential. As the number of network nodes increasing with time interval (or level number), t, the clust...

On the tutte polynomial of benzenoid chains

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.

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 ...

On Szeged Polynomial of a Graph