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Enumeration of rooted loopless Eulerian planar maps. (English) Zbl 1313.05177
Summary: Although much work has been done on enumerating rooted planar maps since Tutte’s pioneering works in early 1960s, many classes of maps with no loops are still untreated. In this paper, we enumerate rooted loopless Eulerian planar maps with three parameters: the valency of rooted vertex, the number of nonrooted vertices and the number of inner faces.
MSC:
05C30 Enumeration in graph theory
05C45 Eulerian and Hamiltonian graphs
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