A new branch of enumerative graph theory
W. T. Tutte · Bulletin of the American Mathematical Society · 1962
In a recent survey [ l ] F. Harary pointed out that the problem of enumerating planar graphs was important but still untouched. I am happy to be able to announce some results in this hitherto neglected field. The results concern rooted maps, that is planar maps in which one edge is selected as the root, a positive sense of description is assigned to it and its two sides are distinguished as right and left. Thus a completely unsymmetrical map of n edges gives rise to just 4n rooted maps. The number of combinatorially distinct rooted maps of n g: 1 edges is 2(2n)\3 (1) n\(n+ 2)!