Let Ng(f ) denote the number of rooted maps of genus g having f edges. An exact formula for Ng(f ) is known for g = 0 (Tutte, 1963), g = 1 (Arques, 1987), g = 2,3 (Bender and Canf...
A map is a connected topological graph cellularly embedded in a surface. For a given graph , its genus distribution of rooted maps and embeddings on orientable and non-orientable s...