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The λ3-connectivity and κ3-connectivity of recursive circulants

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  • Li, Hengzhe
  • Wang, Jiajia

Abstract

Let S be a set of at least two vertices in a graph G. A subtree T of G is a S-Steiner tree if S ⊆ V (T). Two S-Steiner trees T1 and T2 are edge-disjoint (resp. internally disjoint) if E(T1)∩E(T2)=∅ (resp. E(T1)∩E(T2)=∅ and V(T1)∩V(T2)=S). Let λG(S) (resp. κG(S)) be the maximum number of edge-disjoint (resp. internally disjoint) S-Steiner trees in G, and let λk(G) (κk(G)) be the minimum λG(S) (resp. κG(S)) for S ranges over all k-subsets of V(G). Clearly, λ2(G) (resp. κ2(G)) is the classical edge-connectivity λ(G) (resp. connectivity κ(G)). In this paper, we study the λ3-connectivity and κ3-connectivity of a recursive circulant G, determine λ3(G)=δ(G)−1 for each recursive circulant G, and κ3(G)=δ(G)−1 for each recursive circulant G except G≅G(2m, 2).

Suggested Citation

  • Li, Hengzhe & Wang, Jiajia, 2018. "The λ3-connectivity and κ3-connectivity of recursive circulants," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 750-757.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:750-757
    DOI: 10.1016/j.amc.2018.07.065
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    References listed on IDEAS

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    1. Yuefang Sun & Xueliang Li, 2017. "On the difference of two generalized connectivities of a graph," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 283-291, January.
    2. Shasha Li & Xueliang Li, 2012. "Note on the hardness of generalized connectivity," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 389-396, October.
    3. Li, Shasha & Tu, Jianhua & Yu, Chenyan, 2016. "The generalized 3-connectivity of star graphs and bubble-sort graphs," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 41-46.
    4. Li, Hengzhe & Ma, Yingbin & Yang, Weihua & Wang, Yifei, 2017. "The generalized 3-connectivity of graph products," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 77-83.
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