Geodesic
The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces
Izvestiya. Mathematics , Tome 72 (2008) no. 4, pp. 627-646.

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We extend the definition of Hurwitz numbers to the case of seamed surfaces, which arise in new models of mathematical physics, and prove that they form a system of correlators for a Klein topological field theory in the sense defined in [1]. We find the corresponding Cardy–Frobenius algebras, which yield a method for calculating the Hurwitz numbers. As a by-product, we prove that the vector space generated by the bipartite graphs with $n$ edges possesses a natural binary operation that makes this space into a non-commutative Frobenius algebra isomorphic to the algebra of intertwining operators for a representation of the symmetric group $S_n$ on the space generated by the set of all partitions of a set of $n$ elements. 
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A. V. Alekseevskii; S. M. Natanzon. The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces. Izvestiya. Mathematics , Tome 72 (2008) no. 4, pp. 627-646. http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a0/

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