近三正则3—连通平面地图的计数

本文提供了便于依根点次,边数和根面次计数近三正则3－连通有根平面地图的一个函数方程,继之得到其参数形式解,并由此通过Lagrange反演导出了它的计数显示,本文推广了[3]和[4]的结果。     

关于（ξ,k）—临界图

设G为连通图,且ξ（G）=k≥1,若对G中任意边e,均有ξ（G\e）=k-1,则称G为(ξ,k)-临界图。本文刻划了ξ-1-临界图的若干性质,给出了一个图为ξ-1-临界图的一些充分或必要条件,以及一些ξ-1-临界图类。     

ENUMERATING ROOTED EULERIAN PLANAR MAPS

1 IntroductionSince Thtte's papers oll enunlerating planar InaPs in [7,8] published iu the beginlling Ofsixties, the enumerative theory has been developed greatly up to now. The enumeration ofgenera1 Eulerian planar maps is dependent on two paranleters as the valency of rooted vertexalld the uunther of edges Of the nmps. Y.P.Liu found tl1e functional equation firstly for thenlaPs aud then obtained the number of general rooted Elllerian planar maPs with the nuntherof edges given in 1989[1].…