Advances and Applications in Discrete Mathematics
Volume 17, Issue 4, Pages 373 - 382
(October 2016) http://dx.doi.org/10.17654/AADMOct2016_373_382 |
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COUNTING UNICURSAL PLANAR NEAR-TRIANGULATION
Shude Long and Junliang Cai
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Abstract: 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. |
Keywords and phrases: unicursal map, near-triangulation, enumerating function, functional equation.
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