Counting rooted near-triangulations on the sphere (Q1313966)

``This paper provides the results on the enumerations of rooted simple outerplanar maps, rooted outerplanar near-triangulations, rooted 2- connected near-triangulations, rooted strict 2-connected near- triangulations, and rooted simple 2-connected near-triangulations. The answer to an open problem proposed by one of the authors is also provided.'' While the authors have cited a review article by \textit{W. T. Tutte} [Counted rooted triangulations, Ann. Discrete Math. 12, 243-253 (1982; Zbl 0493.05032)], they have evidently not read the last sentence of that paper, to wit, ``More information about the enumeration of triangulations and near-triangulations can be found in papers of W. G. Brown and R. C. Mullin.'' For example, the main result of \S4 is equivalent to equation (4.7) of the reviewer's paper [Enumeration of triangulations of the disk, Proc. Lond. Math. Soc., III. Ser. 14, 746-768 (1964; Zbl 0134.195)].