| 折叠超立方体的广义3-连通度 |
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| 引用本文： | 王军震,张淑敏,葛慧芬. 折叠超立方体的广义3-连通度[J]. 山东大学学报(理学版), 2022, 57(11): 42-49. DOI: 10.6040/j.issn.1671-9352.0.2021.518 |
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| 作者姓名： | 王军震 张淑敏 葛慧芬 |
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| 作者单位： | 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 |
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| 基金项目： | 青海省自然科学基金资助项目(2019-ZJ-921) |
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| 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 ')=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κk(G)=min{κ(S)|S⊆V(G)且|S|=k},显然,κ2(G)=κ(G)。证明了κ3(FQn)=n,其中FQn是n-维折叠超立方体。
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| 关 键 词： | 广义连通度 斯坦纳树 折叠超立方体 |
Generalized 3-connectivity of folded hypercubes |
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| WANG Jun-zhen,ZHANG Shu-min,GE Hui-fen. Generalized 3-connectivity of folded hypercubes[J]. Journal of Shandong University, 2022, 57(11): 42-49. DOI: 10.6040/j.issn.1671-9352.0.2021.518 |
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| Authors: | WANG Jun-zhen ZHANG Shu-min GE Hui-fen |
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| Affiliation: | 1. College of Mathematics and Statistics, Qinghai Normal University, Xining 810008, Qinghai, China;2. Academy of Plateau, Science and Sustainability, Xining 810008, Qinghai, China;3. College of Computing, Qinghai Normal University, Xining 810008, Qinghai, China |
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| Abstract: | 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 ')= 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 κk(G)=min{κ(S)|S⊆V(G)and |S|=k}. Clearly, κ2(G)=κ(G). κ3(FQn)=n is proved where FQn is n-dimensional folded hypercube. |
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| Keywords: | generalized connectivity Steiner tree folded hypercube |
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