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Counting rooted nonseparable unicursal planar maps. (English) Zbl 1424.05153
Summary: A map is unicursal if all its vertices are even-valent except two odd-valent vertices. This paper investigates the enumeration of rooted nonseparable unicursal planar maps and provides two functional equations satisfied by its generating functions with the number of nonrooted vertices, the number of inner faces (or the number of edges) and the valencies of the two odd vertices of maps as parameters.
05C30 Enumeration in graph theory
05C45 Eulerian and Hamiltonian graphs
05C10 Planar graphs; geometric and topological aspects of graph theory