5- ESSENTIAL ROOTED MAPS ON N5

摘要

A g- essential rooted map M on the nonorientable surface Ng with genus g is a map embedded on Ng such that M - e is either not a map or a map not embedded on Ng for any edge e of M. In the paper, we first present the explicit formula of counting 5- essential rooted maps on N5 with the size as a parameter. Furthermore, the number of singular maps and bouquet maps on N5 are derived.