[1] Askanazi, R., Chmutov, S., Estill, C., Michel, J. and Stollenwerk, P. (2013) Polynomial invariants of graphs on surfaces. Quantum Topol. 4 77–90.
[2] Biggs, N. (1993) Algebraic Graph Theory, second edition, Cambridge Mathematical Library, Cambridge University Press.
[3] Bollobás, B. (1998) Modern Graph Theory, Vol. 184 of Graduate Texts in Mathematics, Springer.
[4] Bollobás, B. and Riordan, O. (2001) A polynomial invariant of graphs on orientable surfaces. Proc. London Math. Soc. (3) 83 513–531.
[5] Bollobás, B. and Riordan, O. (2002) A polynomial of graphs on surfaces. Math. Ann. 323 81–96.
[6] Bouchet, A. (1989) Maps and ▵-matroids. Discrete Math. 78 59–71.
[7] Butler, C. (2018) A quasi-tree expansion of the Krushkal polynomial. Adv. in Appl. Math., 94 3–22.
[8] Champanerkar, A., Kofman, I. and Stoltzfus, N. (2011) Quasi-tree expansion for the Bollobás–Riordan–Tutte polynomial. Bull. Lond. Math. Soc. 43 972–984.
[9] Chun, C., Moffatt, I., Noble, S. and Rueckeriemen, R. (2016) Matroids, delta-matroids and embedded graphs. arXiv:1403.0920
[10] DeVos, M. J. (2000) Flows on graphs. PhD thesis, Princeton University.
[11] Edmonds, J. K. (1960) A Combinatorial Representation for Polyhedral Surfaces, Notices of the American Mathematical Society, AMS.
[12] Ellis-Monaghan, J. A. and Merino, C. (2011) Graph polynomials and their applications I: The Tutte polynomial. In Structural Analysis of Complex Networks, Birkhäuser/Springer, pp. 219–255.
[13] Ellis-Monaghan, J. A. and Moffatt, I. (2013) Graphs on Surfaces, Springer Briefs in Mathematics, Springer.
[14] Ellis-Monaghan, J. A. and Moffatt, I. (2015) The Las Vergnas polynomial for embedded graphs. European J. Combin. 50 97–114.
[15] Frobenius, G. (1896) Über Gruppencharaktere. Sitzber. Königlich Preuss Akad. Wiss. Berlin, pp. 985–1021.
[16] Goodall, A., Litjens, B., Regts, G. and Vena, L. (2017) A Tutte polynomial for non-orientable maps. Electron. Notes Discrete Math. 61 513–519.
[17] Hatcher, A. (2002) Algebraic Topology, Cambridge University Press.
[18] Jones, G. A. (1998) Characters and surfaces: A survey. In The Atlas of Finite Groups: Ten Years On, Vol. 249 of London Mathematical Society Lecture Note Series, Cambridge University Press, pp. 90–118.
[19] Kochol, M. (2002) Polynomials associated with nowhere-zero flows. J. Combin. Theory Ser. B 84 260–269.
[20] Krushkal, V. (2011) Graphs, links, and duality on surfaces. Combin. Probab. Comput. 20 267–287.
[21] Lando, S. K. and Zvonkin, A. K. (2004) Graphs on Surfaces and their Applications, Vol. 141 of Encyclopaedia of Mathematical Sciences, Springer.
[22] Las Vergnas, M. (1978) Sur les activités des orientations d'une géométrie combinatoire. Cahiers Centre Études Rech. Opér. 20 293–300.
[23] Las Vergnas, M. (1980) On the Tutte polynomial of a morphism of matroids, Ann. Discrete Math. 8 7–20.
[24] Litjens, B. (2017) On dihedral flows in embedded graphs. arXiv:1709.06469
[25] Litjens, B. and Sevenster, B. Partition functions and a generalized coloring-flow duality for embedded graphs. J. Graph Theory. http://doi.org/10.1002/jgt.22210 [26] Mednyh, A. D. (1978) Determination of the number of nonequivalent coverings over a compact Riemann surface. Dokl. Akad. Nauk SSSR 239 269–271.
[27] Mulase, M. and Yu, J. T. (2005) Non-commutative matrix integrals and representation varieties of surface groups in a finite group. Ann. Inst. Fourier (Grenoble) 55 2161–2196.
[28] Noble, S. D. and Welsh, D. J. A. (1999) A weighted graph polynomial from chromatic invariants of knots. Ann. Inst. Fourier (Grenoble) 49 1057–1087.
[29] Oxley, J. G. and Welsh, D. J. A. (1979) The Tutte polynomial and percolation. In Graph Theory and Related Topics (Bondy, J. A. et al., eds), Academic Press, pp. 329–339.
[30] Serre, J.-P. (2012) Linear Representations of Finite Groups, Vol. 42 of Graduate Texts in Mathematics, Springer.
[31] Tutte, W. T. (1947) A ring in graph theory. Proc. Cambridge Philos. Soc. 43 26–40.
[32] Tutte, W. T. (1949) On the imbedding of linear graphs in surfaces. Proc. London Math. Soc. (2) 51 474–483.
[33] Tutte, W. T. (1954) A contribution to the theory of chromatic polynomials. Canad. J. Math. 6 80–91.
[34] Tutte, W. T. (2001) Graph Theory, Vol. 21 of Encyclopedia of Mathematics and its Applications, Cambridge University Press.
[35] Tutte, W. T. (2004) Graph-polynomials. Adv. Appl. Math. 32 5–9.
[36] Watanabe, Y. and Fukumizu, K. (2011) New graph polynomials from the Bethe approximation of the Ising partition function. Combin. Probab. Comput. 20 299–320.
[37] Welsh, D. J. A. (1993) Complexity: Knots, Colourings and Counting, Vol. 186 of London Mathematical Society Lecture Note Series, Cambridge University Press.
[38] Welsh, D. J. A. (1999) The Tutte polynomial. Random Struct. Alg. 15 210–228.
[39] Whitney, H. (1932) Non-separable and planar graphs. Trans. Amer. Math. Soc. 34 339–362.
