超限制边连通笛卡尔乘积图的边容错性(英文)  

Edge fault-tolerance of super restricted edge-connected Cartesian product graphs

作　　者：洪振木[1,2] 徐俊明[1,2] 

机构地区：[1]中国科学技术大学数学科学学院 [2]中国科学院吴文俊数学重点实验室,安徽合肥230026

出　　处：《中国科学技术大学学报》2014年第12期967-974,共8页JUSTC

基　　金：Supported by NSFC(61272008)

摘　　要：如果G-F不连通且每个连通分支至少含有两个顶点,则连通图G的边子集F称为限制边割.如果图G的每个最小限制边割都孤立G中的一条边,则称G是超限制边连通的(简称超λ′).对于满足|F|≤m的任意子集FE(G),超λ′图G的边容错性ρ′(G)是使得G-F仍是超λ′的最大整数m.这里给出了min{k1+k2-1,υ1k2-2k1-2k2+1,υ2k1-2k1-2k2+1}≤ρ′(G1×G2)≤k1+k2-1,其中,对每个i∈{1,2},Gi是阶为υi的ki正则ki边连通图且ki≥4,G1×G2是G1和G2的笛卡尔乘积.并给出了使得ρ′(G1×G2)=k1+k2-1的一些充分条件.A subset F of edges in a connected graph G is a restricted edge-cut if G-F is disconnected and every component has at least two vertices.A graph Gis super restricted edgeconnected（super-λ′for short）if every minimum restricted edge-cut of Gisolates at least one edge.The edge fault-toleranceρ′（G）of a super-λ′graph Gis the maximum integer mfor which G-Fis still super-λ′for any subset F E（G）with｜F｜≤m.It was shown that min{k1＋k2-1,υ1k2-2k1-2k2 ＋1,υ2k1-2k1-2k2 ＋1}≤ρ′（G1×G2）≤k1 ＋k2-1,where Giis a ki-regular ki-edge-connected graph of orderυi with ki≥4for each i∈ {1,2}and G1×G2is the Cartesian product graph of G1 and G2.And some sufficient conditions such thatρ′（G1×G2）=k1＋k2-1were presented.

关 键 词：图 连通度 容错性 超限制边连通 笛卡尔乘积 正则图 网络 

分 类 号：O157.5[理学—数学] TP302.8[理学—基础数学]