(k,l)-递归极大平面图的结构

陈祥恩; 李婷

doi:10.11999/JEIT171021

(k,l)-递归极大平面图的结构

doi: 10.11999/JEIT171021

陈祥恩^,,
李婷

西北师范大学数学与统计学院兰州 730070

基金项目: 国家自然科学基金(11761064, 61163037, 61163054)

详细信息

作者简介:
陈祥恩：男，1965年生，教授，主要研究方向为图论及其应用

李婷：女，1993年生，硕士生，研究方向为图论及其应用

通讯作者:
陈祥恩　 chenxe@nwnu.edu.cn

中图分类号: O157.5
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- 文章访问数: 1688
- HTML全文浏览量: 662
- PDF下载量: 30
- 被引次数: 0
出版历程
- 收稿日期: 2017-11-01
- 修回日期: 2018-06-04
- 网络出版日期: 2018-07-12
- 刊出日期: 2018-09-01

The Structure of (k,l)-recursive Maximal Planar Graph

Xiang’en CHEN^,,
Ting LI

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Funds: The National Natural Science Foundation of China (11761064, 61163037, 61163054)

摘要

摘要: 对于一个平面图G实施扩3-轮运算是指在G的某个三角形面xyz内添加一个新顶点v，使v与x, y, z均相邻，最后得到一个阶为|V(G)|+1的平面图的过程。一个递归极大平面图是指从平面图K₄出发，逐次实施扩3-轮运算而得到的极大平面图。所谓一个(k,l)-递归极大平面图是指一个递归极大平面图，它恰好有k个度为3的顶点，并且任意两个3度顶点之间的距离均为l。该文对(k,l)-递归极大平面图的存在性问题做了探讨，刻画了(3,2)-及(2,3)-递归极大平面图的结构。
- 平面图 /
- 极大平面图 /
- 扩3-轮 /
- 递归极大平面图
Abstract: For a maximal planar graph G, the operation of extending 3-wheel is a process from G to G∨v, where v is a new vertex embedded in some triangular face xyz of G and G∨v is a graph of order |V(G)|+1 obtained from G by connecting v to each one of x, y, z with one edge. A recursive maximal planar graph is a maximal planar graph obtained from K₄ by extending 3-wheel continuously. A (k,l)-recursive maximal planar graph is a recursive maximal planar graph with exactly k vertices of degree 3 so that the distance between arbitrary two vertices of degree k is l. The existence of (k,l)-recursive maximal planar graph is discussed and the structures of (3,2)-as well as (2,3)-recursive maximal planar graphs are described.
- Planar graph /
- Maximal planar graph /
- Extending 3-wheel /
- Recursive maximal planar graph

HTML全文

图 1 阶分别为4,7,10的递归极大平面图

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图 2 命题3所述图的结构

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图 3 命题3证明过程中出现的递归极大平面图

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图 4 定理4证明过程中出现的递归极大平面图

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图 5 A型的(2,3)-递归极大平面图

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图 6 6阶的B型(2,3)-递归极大平面图

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图 7 定理7证明里(1)中的B型(2,3)-递归极大平面图

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图 8 定理7证明里(2)中出现的(2,3)-递归极大平面图

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图 9 定理7证明里(2)中出现的另一个(2,3)-递归极大平面图

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图 10 C型的(2,3)-递归极大平面图

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图 11 A型递归极大平面图

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图 12 B型的(3,2)-递归极大平面图

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图 13 C型的(3,2)-递归极大平面图

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图 14 D型的(3,2)-递归极大平面图

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