On some properties of vector space based graphs

Peter J. Cameron; Angsuman Das; Hiranya Kishore Dey

doi:10.1080/03081087.2022.2121370

On some properties of vector space based graphs

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	2858-2868
Number of pages	11
Journal	Linear and Multilinear Algebra
Volume	71
Issue number	17
Early online date	13 Sept 2022
DOIs	https://doi.org/10.1080/03081087.2022.2121370
Publication status	Published - 2023

Keywords

Maximal intersecting family
Hamiltonian
Base

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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.
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Cite this

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title = "On some properties of vector space based graphs",

abstract = "In this paper, we study some problems related to subspace inclusion graph ℐn(핍) and subspace sum graph 풢(핍) of a finite-dimensional vector space 핍. Namely, we prove that ℐn(핍) is a Cayley graph as well as Hamiltonian when the dimension of 핍 is 3. We also find the exact value of independence number of 풢(핍) when the dimension of 핍 is odd. The above two problems were left open in previous works in the literature. Moreover, we prove that the determining numbers of ℐn(핍) and 풢(핍) are bounded above by 6. Finally, we study some forbidden subgraphs of these two graphs.",

keywords = "Maximal intersecting family, Hamiltonian, Base",

author = "Cameron, {Peter J.} and Angsuman Das and Dey, {Hiranya Kishore}",

note = "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. ",

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AU - Cameron, Peter J.

AU - Das, Angsuman

AU - Dey, Hiranya Kishore

N1 - 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.

PY - 2023

Y1 - 2023

N2 - In this paper, we study some problems related to subspace inclusion graph ℐn(핍) and subspace sum graph 풢(핍) of a finite-dimensional vector space 핍. Namely, we prove that ℐn(핍) is a Cayley graph as well as Hamiltonian when the dimension of 핍 is 3. We also find the exact value of independence number of 풢(핍) when the dimension of 핍 is odd. The above two problems were left open in previous works in the literature. Moreover, we prove that the determining numbers of ℐn(핍) and 풢(핍) are bounded above by 6. Finally, we study some forbidden subgraphs of these two graphs.

AB - In this paper, we study some problems related to subspace inclusion graph ℐn(핍) and subspace sum graph 풢(핍) of a finite-dimensional vector space 핍. Namely, we prove that ℐn(핍) is a Cayley graph as well as Hamiltonian when the dimension of 핍 is 3. We also find the exact value of independence number of 풢(핍) when the dimension of 핍 is odd. The above two problems were left open in previous works in the literature. Moreover, we prove that the determining numbers of ℐn(핍) and 풢(핍) are bounded above by 6. Finally, we study some forbidden subgraphs of these two graphs.

KW - Maximal intersecting family

KW - Hamiltonian

KW - Base

U2 - 10.1080/03081087.2022.2121370

DO - 10.1080/03081087.2022.2121370

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JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

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ER -

On some properties of vector space based graphs

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Keywords

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