对偶图是与平面图相伴的一种图。对于给定平面图G=〈V,E〉,设G的面为F₁,F₂,…,Fₑ,当图G*满足如下条件时,则图G*=〈V*,E*〉称为G的对偶图: ①对G的每个面Fₒ,内部任选一点v*ₒ∈V*; ②对Fₒ,Fₓ的每一条公共边界eₔ,vₒ*与vₓ*间有一条边eₔ*,并且eₔ*与eₔ交于一点; ③当且仅当eₔ仅是一个面Fₒ的边界时,vₒ*有一个环(自回路),eₒ*与eₔ相交。
本文论述了自对偶图和简单自对偶图的一些性质。
This paper discusses some properties of the Self-dual graph and simple self-dual graph.
阐明了平图中的H圈与对偶图顶点四着色的依存关系。
The interdependent relationship between the Hamiltonian cycle and 4-colouring of the planar graph in the dual have discussed.
给出自对偶图的充要条件,并利用此充要条件,能构造出所有自对偶图。
The paper gives the necessary and sufficient condition of self-dual graphs, all of self-dual graphs can be structured with this necessary and sufficient codition.
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