关于网络的控制数的几点注记  

Some remarks about dominating number of network

作　　者：郝建修[1] HAO Jianxiu(Institute of Mathematics and Computer Sciences,Zhejiang Normal University,Jinhua 321004,Zhejiang,China)

机构地区：[1]浙江师范大学数学与计算机学院,浙江金华321004

出　　处：《运筹学学报》2023年第3期185-190,共6页Operations Research Transactions

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。(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.

关 键 词：(d w)-控制数 超立方体 网络 组合问题 

分 类 号：O157.5[理学—数学]