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On the P3-hull numbers of q-Kneser graphs and Grassmann graphs

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  • Liao, Jiaqi
  • Cao, Mengyu
  • Lu, Mei

Abstract

Let S be an n-dimensional vector space over the finite field Fq, where q is necessarily a prime power. Denote Kq(n,k) (resp. Jq(n,k)) to be the q-Kneser graph (resp. Grassmann graph) for k⩾1 whose vertices are the k-dimensional subspaces of S and two vertices v1 and v2 are adjacent if dim(v1∩v2)=0 (resp. dim(v1∩v2)=k−1). We consider the infection spreading in the q-Kneser graphs and the Grassmann graphs: a vertex gets infected if it has at least two infected neighbors. In this paper, we compute the P3-hull numbers of Kq(n,k) and Jq(n,k) respectively, which is the minimum size of a vertex set that eventually infects the whole graph.

Suggested Citation

  • Liao, Jiaqi & Cao, Mengyu & Lu, Mei, 2023. "On the P3-hull numbers of q-Kneser graphs and Grassmann graphs," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    • Handle: RePEc:eee:apmaco:v:437:y:2023:i:c:s0096300322006105
    DOI: 10.1016/j.amc.2022.127536
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    References listed on IDEAS

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    1. Wayne Pullan & Xin-Wen Wu & Zihui Liu, 2016. "Construction of optimal constant-dimension subspace codes," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1709-1719, May.
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    Cited by:

    1. Bedo, Marcos & Leite, João V.S. & Oliveira, Rodolfo A. & Protti, Fábio, 2023. "Geodetic convexity and kneser graphs," Applied Mathematics and Computation, Elsevier, vol. 449(C).

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      Keywords

      P3-hull number; q-Kneser graph; Grassmann graph;
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