极大外平面图的Wiener指标的上下界

孙晓慧; 安新慧

doi:10.13568/j.cnki.651094.651316.2023.01.04.0001

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极大外平面图的Wiener指标的上下界

更新时间：2026-01-21

- 极大外平面图的Wiener指标的上下界
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 40, Issue 5, Pages: 560-564(2023)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2023.01.04.0001
  CLC： O157.5
- Published：2023
- 稿件说明：
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[1]孙晓慧,安新慧.极大外平面图的Wiener指标的上下界[J].新疆大学学报(自然科学版)(中英文),2023,40(05):560-564.
[1]孙晓慧,安新慧.极大外平面图的Wiener指标的上下界[J].新疆大学学报(自然科学版)(中英文),2023,40(05):560-564. DOI： 10.13568/j.cnki.651094.651316.2023.01.04.0001.

DOI：10.13568/j.cnki.651094.651316.2023.01.04.0001.

摘要

外平面图是具有平面嵌入的平面图

其中每个顶点位于外部区域的边界上.若通过添加边获得的图不是外平面图

则此时的外平面图是极大外平面图.图G的Wiener指标是所有顶点对之间距离的总和.证明了对于n个顶点的极大外平面图G

有W(K1∨Pn-1)≤W (G)≤W (Pn~2)

其中K1∨Pn-1是通过将一个点和路Pn-1的每个顶点相连得到的图

Pn~2是路的平方图.

Abstract

A graph is outerplanar if it has a crossing-free embedding in the plane such that all vertices are on the boundary of its outer face. An outerplanar graph is maximal outerplanar if no edge can be added without losing outerplanarity. The Wiener index of a graph G is the sum of distances between all pairs of vertices of G. We show that for a maximal outerplanar graph G on n vertices

W(K1∨Pn-1)≤W (G)≤W (Pn~2)

where K1 ∨Pn-1 is the graph obtained from joining a vertex to each vertex of Pn-1and Pn2is the square of Pn.

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references

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