n维无向超环面网的(l,2n)控制数  

On the(l,2n)-domination Number of the n-dimensional Undirected Toroidal Mesh

作　　者：谢歆 项诗景 XIE Xin;XIANG Shijing(School of Mathematics and Statistics, Huangshan University, Huangshan Anhui 245041, China;School of Mathematical Sciences, Huaqiao University, Quanzhou Fujian 362021, China)

机构地区：[1]黄山学院数学与统计学院,安徽黄山245041 [2]华侨大学数学科学学院,福建泉州362021

出　　处：《复旦学报（自然科学版）》2020年第2期149-155,共7页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金(11961019);2019年度安徽省高校学科(专业)拔尖人才学术资助项目(2019gxbjZD38)。

摘　　要：对于m连通图G,宽直径dm(G)是指最小正整数d使得图G中任何两顶点x和y间都存在m条内点不交且每条长度不超过d的路.顶点集V(G)的子集S称作(l,m)控制集,如果顶点■x∈V(G)-S,都存在m条从S到x内点不交且每条长度不超过l的路.G的所有(l,m)控制集中顶点个数的最小值称为(l,m)控制数.若「f(d1,d2,…,dn)」+3≤l≤dG(C(d1,d2,…,dn),可知无向超环面网C(d1,d2,…,dn)的(l,2n)控制数为2,其中f(d1,d2,…,dn)=1/2■e’i,n≥4,di≥5(i=1,2,…,n).For an m-connected graph G,the m-wide diameter dm(G) is the minimum integer d such that for any two vertices x and y in G,there are at least m internally vertex-disjoint paths of length at most d from x to y.A subset S of V(G) is called a(l,m)-dominating set of G if for any vertex x∈V(G)-S,there are at least m internally vertex-disjoint paths of length at most l from S to x.The minimum cardinality among all(l,m)-dominating sets of G is called the(l,m)-domination number.This paper proves that the(l,2 n)-domination number of C(d1,d2,…,dn) is 2 for「f(d1,d2,…,dn)(C(d1,d2,…,dn)) with f(d1,d2,…,dn)=1/2■e’i,for n≥4 and,di≥5(i=1,2,…,n).

关 键 词：无向超环面网 控制数 宽直径 可靠性 

分 类 号：O157.5[理学—数学]