On some properties of vector space based graphs

Peter J. Cameron, Angsuman Das*, Hiranya Kishore Dey

*Corresponding author for this work

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Abstract

In this paper, we study some problems related to subspace inclusion graph ℐn(𝕍) and subspace sum graph 𝒢(𝕍) of a finite-dimensional vector space 𝕍. Namely, we prove that ℐn(𝕍) is a Cayley graph as well as Hamiltonian when the dimension of 𝕍 is 3. We also find the exact value of independence number of 𝒢(𝕍) when the dimension of 𝕍 is odd. The above two problems were left open in previous works in the literature. Moreover, we prove that the determining numbers of ℐn(𝕍) and 𝒢(𝕍) are bounded above by 6. Finally, we study some forbidden subgraphs of these two graphs.
Original languageEnglish
Pages (from-to)2858-2868
Number of pages11
JournalLinear and Multilinear Algebra
Volume71
Issue number17
Early online date13 Sept 2022
DOIs
Publication statusPublished - 2023

Keywords

  • Maximal intersecting family
  • Hamiltonian
  • Base

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