On some properties of vector space based graphs
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In this paper, we study some problems related to subspace inclusion graph ℐn() and subspace sum graph () of a finite-dimensional vector space . Namely, we prove that ℐn() is a Cayley graph as well as Hamiltonian when the dimension of is 3. We also find the exact value of independence number of () when the dimension of is odd. The above two problems were left open in previous works in the literature. Moreover, we prove that the determining numbers of ℐn() and () are bounded above by 6. Finally, we study some forbidden subgraphs of these two graphs.
Cameron , P J , Das , A & Dey , H K 2023 , ' On some properties of vector space based graphs ' , Linear and Multilinear Algebra , vol. 71 , no. 17 , pp. 2858-2868 . https://doi.org/10.1080/03081087.2022.2121370
Linear and Multilinear Algebra
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DescriptionFunding: The second author acknowledges the funding of DST grants no. SRG/2019/000475 and SR/F ST/MS − I/2019/41, Govt. of India. The third author acknowledges Department of Atomic Energy, Government of India for the financial support and Harish-Chandra Research Institute for the research facilities provided.
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