English

运筹学学报 ›› 2023, Vol. 27 ›› Issue (3): 185-190.doi: 10.15960/j.cnki.issn.1007-6093.2023.03.016

•   • 上一篇    

关于网络的控制数的几点注记

郝建修()   

  1. 浙江师范大学 数学与计算机学院, 浙江金华 321004
  • 收稿日期:2019-05-13 出版日期:2023-09-15 发布日期:2023-09-14
  • 通讯作者: 郝建修 E-mail:sx35@zjnu.cn
  • 作者简介:郝建修, E-mail: sx35@zjnu.cn

Some remarks about dominating number of network

Jianxiu HAO()   

  1. Institute of Mathematics and Computer Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
  • Received:2019-05-13 Online:2023-09-15 Published:2023-09-14
  • Contact: Jianxiu HAO E-mail:sx35@zjnu.cn

RichHTML

2

PDF

118

摘要：

(d, w)-控制数是一个度量共享网络资源的可靠性的重要参数。(1, 1)-控制数就是图论中的经典控制数, (d, w)-控制数是(1, 1)-控制数的一个直接推广。本文给出了计算(1, w)-控制数的一个下界方法和一个上界方法。应用这两个方法, 求出了超立方体的(1, n-1)-控制数和(1, n)-控制数, 求出了4基n立方体的(1, 2n - 1) -控制数和(1, 2n)-控制数, 求出了n维折叠超立方体的(1, n)-控制数。

关键词: (d, w)-控制数, 超立方体, 网络, 组合问题

Abstract:

(d, w) -dominating number is an important measuring parameter for the reliability of sharing common source in a network. (1, 1) -dominating number is also known as dominating number which is a classical parameter in graph theory. (d, w) -dominating number is a simple generalization of (1, 1) -dominating number. In this paper we present a lower bound and an upper bound for the calculating of (1, w) -dominating number. Using these two bounds, we find the (1, n - 1)-dominating number and (1, n)-dominating number for hypercube, we find the (1, 2n - 1) -dominating number and (1, 2n)-dominating number for 4-ary n-cube, and the (1, n)-dominating number for n dimensional folded hypercube.

Key words: (d, w)-dominating number, hypercube, network, combinatorial problem

中图分类号: