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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (12): 103-110.doi: 10.6040/j.issn.1671-9352.0.2021.784

• • 上一篇    

笛卡尔乘积图的k-路点覆盖

索孟鸽,陈京荣*,张娟敏   

  1. 兰州交通大学数理学院, 甘肃 兰州 730070
  • 发布日期:2022-12-05
  • 作者简介:索孟鸽(1998— ),女,硕士研究生,研究方向为路覆盖优化.E-mail:1306766428@qq.com*通信作者简介:陈京荣(1975— ),女,博士,教授,研究方向为网络优化理论与算法设计.E-mail:chenjr@mail.lzjtu.cn
  • 基金资助:
    甘肃省自然科学基金资助项目(1610RJZA038)

k-Path vertex cover in Cartesian product graphs

SUO Meng-ge, CHEN Jing-rong*, ZHANG Juan-min   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2022-12-05

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摘要： 对于一个图G和一个正整数k,若图G中任意一条阶数为k的路都至少包含集合S⊆V(G)中的一个顶点,那么集合S就为图G的一个k-路点覆盖。最小的k-路点覆盖基数记为ψk(G),为图G的k-路点覆盖数。研究圈图分别与圈图、完全图及完全二部图做笛卡尔乘积图的k-路点覆盖,得到ψk(G)相关的精确值和上下界。

关键词: k-路点覆盖, 笛卡尔乘积图, 圈图, 完全图, 完全二部图

Abstract: For a graph G and a positive integer k, a subset S⊆V(G)is called a k-path vertex cover if any path of order k in G contains at least one vertex from S. The cardinality of the minimum k-path vertex cover is called the k-path vertex cover number of graph G, denoted by ψk(G). The k-path vertex cover problem of Cartesian product graphs in cycle graph and cycle graph, cycle graph and complete graph, cycle graph and complete bipartite graph is studied, and the exact value, upper or lower bound of ψk(G)is obtained.

Key words: k-path vertex cover, Cartesian product graph, cycle graph, complete graph, complete bipartite graph

中图分类号: 

  • O157.5
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