六边形堆砌的莫比乌斯图的Wiener指标

摘要

Wiener index is a more important topological index in theoretical chemistry. Physical chemical properties of material are closely related to this index. Hexagonal Mobius graphs are one type of molecular graphs embedded into the Mobius strip such that each face is a hexagon. Firstly, via the orbits of automorphism of graphs,the vertex sets of the two special class of hexagonal Mobius graphs were divided. Then taking one representative in every part,all the distances from other vertices to it were summed. Finally,an explicit formula of Wiener index of the hexagonal Mobius graphs was obtained.%Wiener指标是理论化学里比较重要的一个拓扑指标,物质的很多物理化学性质与之有密切的联系.六边形堆砌的莫比乌斯图是一种嵌入到莫比乌斯带上使得每个面都是六边形的分子图.首先,利用图的自同构群的轨道理论,对两类特殊的六边形堆砌的莫比乌斯图的顶点进行了划分.然后在划分的每个类中各取一个代表元,计算其他各点到它的距离和,从而得到了六边形堆砌的莫比乌斯分子图Wiener指标的精确计算公式.