12阶的(4,8)-正则极大平面图的不存在性

The Nonexistence of (4,8)-Regular Maximal Planar Graph on 12 Vertives

当图的顶点数n>12时,不存在正则极大平面图。S.Karimi et.al.提出了(r,k)-正则极大平面图的概念,并讨论了(5,6)-正则极大平面图的存在性。作者曾讨论了阶n>12的(k,l)-正则极大平面图的存在条件及构造方法,研究并讨论了阶n(n>12)的(k,l)-正则极大平面图的存在性及其构造,对于剩余的两种情况,同时提出了两个猜想。本文在此基础上又证明了其中一个猜想的正确性——不存在12阶的(4,8)-正则极大平面图。

No maximal planar graphis regular for vertex number n〉12.S.Karimi et.al.raise the conception of（r,k）-regular graphs,and discuss the existence of（5,6）-regular maximal planar graph.we study the（k,l）-regular maximum planar graph on n〉12 vertives,its existence condition and construction method are obtained respectively.And the existence condition and construction of the（k,l）-regular maximum planar graph on（n〉12） vertices are studied and discussed.For the last two conditions,the two conjecture are put forward,On the basis of this,this paper provides sufficient proofs for the correctness of the nonexistence of（4,8）-regular maximal planar graph on 12 vertives.