折叠超立方体的广义3-连通度  

Generalized 3-connectivity of folded hypercubes

作　　者：王军震 张淑敏 葛慧芬 WANG Jun-zhen;ZHANG Shu-min;GE Hui-fen(College of Mathematics and Statistics,Qinghai Normal University,Xining 810008,Qinghai,China;Academy of Plateau,Science and Sustainability,Xining 810008,Qinghai,China;College of Computing,Qinghai Normal University,Xining 810008,Qinghai,China)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810008 [2]高原科学与可持续发展研究院,青海西宁810008 [3]青海师范大学计算机学院,青海西宁810008

出　　处：《山东大学学报（理学版）》2022年第11期42-49,共8页Journal of Shandong University(Natural Science)

基　　金：青海省自然科学基金资助项目(2019-ZJ-921)。

摘　　要：设图G是一个连通图,S⊆V(G)。图G的一棵S-斯坦纳树是一棵包含S中所有顶点的树T=(V′,E′),使得S⊆V′。如果连接S的两棵斯坦纳树T和T′,满足E(T)∩E(T′)=Φ且V(T)∩V(T′)=S,则称T和T′是内部不交的。定义κ(S)为图G中内部不相交S-斯坦纳树的最大数目。广义k-连通度(2≤k≤n)定义为κ_(k)(G)=min{κ(S)|S⊆V(G)且|S|=k},显然,κ_(2)(G)=κ(G)。证明了κ_(3)(FQ_(n))=n,其中FQ_(n)是n-维折叠超立方体。Let G be a connected graph and S⊆V(G).T=(V′,E′)is an S-Steiner tree which containing all the vertices in is S of G and make S⊆V′.Two S-trees T and T′are said to be internally disjoint if E(T)∩E(T′)=Φ and V(T)∩V(T′)=S.κ(S)is defined as the maximum number of the internally disjoint S-trees in G.The generalized k-connectivity(2≤k≤n)κk(G)of G is defined as κ_(k)(G)=min{κ(S)|S⊆V(G)and|S|=k}.Clearly,κ_(2)(G)=κ(G).κ_(3)(FQ_(n))=n is proved where FQ_(n)is n-dimensional folded hypercube.

关 键 词：广义连通度 斯坦纳树 折叠超立方体 

分 类 号：O157[理学—数学]