(1) Dept. of Math., Xiamen Univ., 361005 Xiamen;(2) Dept. of Math., Northern Jiaotong Univ., 100044 Beijing
Abstract:
In this article the rooted planar near-4-regular Eulerian trails are enum erated and an explicit form ula for such m aps is presented. Further, the rooted near-4-regular Eulerian m aps on the torus are counted in an exact w ay.