On some properties of vector space based graphs
Abstract
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.
Citation
Cameron , P J , Das , A & Dey , H K 2022 , ' On some properties of vector space based graphs ' , Linear and Multilinear Algebra , vol. Latest Articles . https://doi.org/10.1080/03081087.2022.2121370
Publication
Linear and Multilinear Algebra
Status
Peer reviewed
ISSN
0308-1087Type
Journal article
Rights
Copyright © 2022 Informa UK Limited, trading as Taylor & Francis Group. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1080/03081087.2022.2121370.
Description
Funding: 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.Collections
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