一类5-正则外平面图的亏格分布

Genus Distribution for a Type of 5-regular Outerplanar Graphs

计算外平面图的亏格分布是拓扑图论关注的一个问题.本文考虑一类5-正则外平面图O_n的亏格分布.由n个基础图(R_1,p,q)迭代粘合可得到一条开放链(R_n,p,q),对图(R_n,p,q)进行修改的加边运算可得到图O_n.本文利用根-图得到了图(R_n,p,q)的部分亏格分布与图O_n的亏格分布的迭代计算公式.

Calculating the genus distributions of outerplanar graphs is a concerned topic in topological graph theory.In this paper,we concider the genus distribution for a type of 5-regular outerplanar graph On.Using rooted-graphs,we derive simultaneous recursions for the partial genus distribution of the graph（Rn,p,q） constructed by an open chain of n copies of a base graph（R_1,p,q）,and a recursion formula for the genus distribution of the graphs O_n formed by modified edge-addition on（R_n,p,q）.