an:06693847
Zbl 1358.05170
Long, Shude; Cai, Junliang
Counting unicursal planar near-triangulation
EN
Adv. Appl. Discrete Math. 17, No. 4, 373-382 (2016).
00362675
2016
j
05C45 05C30 05A15
unicursal map; near-triangulation; enumerating function; functional equation
Summary: A map is unicursal if all its vertices are even-valent except two odd-valent vertices. A near-triangulation is a map with all but one of its face triangles. This paper investigates the enumeration of rooted unicursal planar near-triangulation and provides two functional equations satisfied by its generating functions with the root-face valency, the number of edges and the number of nonrooted vertices of maps as parameters.