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计量
文章访问数:938
HTML全文浏览量:358
PDF下载量:19
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。
关键词: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.
Key words:Planar graph/
Maximal planar graph/
Extending 3-wheel/
Recursive maximal planar graph
PDF全文下载地址:
https://jeit.ac.cn/article/exportPdf?id=207c3b93-3314-4153-bd1f-623b3fb7363d
