圈梯形图序列的嵌入

Embeddings of Circular Ladder-like Graph Families

本文主要研究确定圈梯形图序列和莫比乌斯梯形图序列(由梯形图类生成的图)的亏格分布.首先利用运算矩阵讨论梯形图类的亏格分布,然后利用加边规则,在梯形图类上加边,得到圈梯形图序列或莫比乌斯梯形图序列,进而得到圈梯形图序列(莫比乌斯梯形图序列)的亏格分布.另外,还验证了经典梯图亏格分布的渐近正态性.

We determine the genus distributions for circular ladder-like sequences of graphs and Mobius ladder-like sequences of graphs.First,we obtain the production matrix for genus distributions of ladder-like sequences of graphs.Then,any circular(Mobius)ladder-like graph is obtained by adding edges to a ladder-like graph by using edge addition rule,and we obtain the genus polynomials for circular ladder-like sequences of graphs and Mobius ladder-like sequences of graphs.In addition,we also verify the asymptotic normality of the classical ladder graphs.