JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (11): 42-49.doi: 10.6040/j.issn.1671-9352.0.2021.518

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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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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

CLC Number: 

  • O157
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