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Counting 2-connected 4-regular maps on the projective plane. (English) Zbl 1300.05131
Summary: In this paper the number of rooted (near-) 4-regular maps on the projective plane are investigated with respect to the root-valency, the number of edges, the number of inner faces, the number of nonroot-vertex-loops, the number of nonroot-vertex-blocks. As special cases, formulae for several types of rooted 4-regular maps such as 2-connected 4-regular projective planar maps, rooted 2-connected (connected) 4-regular projective planar maps without loops are also presented. Several known results on the number of 4-regular maps on the projective plane are also concluded. Finally, by use of Darboux’s method, very nice asymptotic formulae for the numbers of those types of maps are given.

05C30 Enumeration in graph theory
05C10 Planar graphs; geometric and topological aspects of graph theory
05C45 Eulerian and Hamiltonian graphs
05C40 Connectivity
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