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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (11): 42-49.doi: 10.6040/j.issn.1671-9352.0.2021.518

• • 上一篇    

折叠超立方体的广义3-连通度

王军震1,张淑敏1,2*,葛慧芬3   

  1. 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
  • 发布日期:2022-11-10
  • 作者简介:王军震(1993— ),男,硕士研究生,研究方向为组合数学与图论.E-mail:wangjunzhen2021@126.com*通信作者简介:张淑敏(1971— ),女,博士,教授,研究方向为组合数学与图论.E-mail:zhangshumin@qhnu.edu.cn
  • 基金资助:
    青海省自然科学基金资助项目(2019-ZJ-921)

Generalized 3-connectivity of folded hypercubes

WANG Jun-zhen1, ZHANG Shu-min1,2*, GE Hui-fen3   

  1. 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
  • Published:2022-11-10

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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。

关键词: 广义连通度, 斯坦纳树, 折叠超立方体

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.

Key words: generalized connectivity, Steiner tree, folded hypercube

中图分类号: 

  • O157
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