Mphako-Banda, Eunice, and Julian A. Allagan. "Formulas for the Computation of the Tutte Polynomial of Graphs with Parallel Classes." Electronic Journal of Graph Theory and Applications, vol. 6, no. 1, 2018, pp. 113-122, doi:10.5614/ejgta.2018.6.1.8.
We give some reduction formulas for computing the Tutte polynomial of any graph with parallel classes. Several examples are given to illustrate our results.