  The Tutte polynomial of a graph, or equivalently the $q$-state Potts model
partition function, is a two-variable polynomial graph invariant of
considerable importance in both combinatorics and statistical physics. The
computation of this invariant for a graph is NP-hard in general. In this paper,
based on their self-similar structures, we recursively describe the Tutte
polynomials of an infinite family of scale-free lattices. Furthermore, we give
some exact analytical expressions of the Tutte polynomial for several special
points at $(X,Y)$-plane.
