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The k-independence number of t-connected graphs

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  • Li, Zhonghua
  • Wu, Baoyindureng

Abstract

A set S⊆V(G) is a k-independent set of a graph G if the distance between every two vertices of S is greater than k. The k-independence number αk(G) of G is the maximum cardinality over all k-independent set in G. In this note, we show that if G is a t-connected graph of order n, then α2k+1(G)≤max{1,n−ttk+1} and α2k(G)≤max{1,ntk+1} for any integer k≥0. Both bounds are sharp. For any integer s≥2,p(G,s)=max{min1≤i≤j≤sd(vi,vj):{v1,…,vs}⊆V(G)},is a generalization of the diameter of G. We determine the exact value of the maximum p(G,s) among all t-connected graphs of order n. This includes the main results of a recent paper by Knor and Škrekovski (On the minimum distance in a k-vertex set in a graph, Appl. Math. Comput. 356 (2019) 99–104) and solve an open problem therein.

Suggested Citation

  • Li, Zhonghua & Wu, Baoyindureng, 2021. "The k-independence number of t-connected graphs," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321005014
    DOI: 10.1016/j.amc.2021.126412
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    References listed on IDEAS

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    1. Knor, Martin & Škrekovski, Riste, 2019. "On the minimum distance in a k-vertex set in a graph," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 99-104.
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    Cited by:

    1. Gaspoz, Sébastien & Maffucci, Riccardo W., 2024. "Independence numbers of polyhedral graphs," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    2. Ahmed Badawy & Jesus A. Fisteus & Tarek M. Mahmoud & Tarek Abd El-Hafeez, 2021. "Topic Extraction and Interactive Knowledge Graphs for Learning Resources," Sustainability, MDPI, vol. 14(1), pages 1-21, December.

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