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We show that any graph polynomial from a wide class of graph polynomialsyields a recurrence relation on an infinite class of families of graphs. Therecurrence relations we obtain have coefficients which themselves satisfylinear recurrence relations. We give explicit applications to the Tuttepolynomial and the independence polynomial. Furthermore, we get that for anysequence $a_{n}$ satisfying a linear recurrence with constant coefficients, thesub-sequence corresponding to square indices $a_{n^{2}}$ and relatedsub-sequences satisfy recurrences with recurrent coefficients.

Recurrence Relations for Graph Polynomials on Bi-iterative Families of Graphs