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

Jiaqi Liao, Mengyu Cao and Mei Lu

Applied Mathematics and Computation, 2023, vol. 437, issue C

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.

Keywords: P3-hull number; q-Kneser graph; Grassmann graph (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:437:y:2023:i:c:s0096300322006105

DOI: 10.1016/j.amc.2022.127536

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