Book thickness of the non-zero component union graph of the finite dimensional vector space

N. Mohamed Rilwan () and S. Vasanthi Devi ()
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N. Mohamed Rilwan: Sadakathullah Appa College, Affiliated to Manonmaniam Sundaranar University
S. Vasanthi Devi: Sadakathullah Appa College, Affiliated to Manonmaniam Sundaranar University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 267-273

Abstract: Abstract The non-zero component union graph $$\Gamma \left( \mathbb {V}_{\mathcal {B}}\right) $$ Γ V B with respect to basis $$\left\{ \alpha _1,\alpha _2,\right. $$ α 1 , α 2 , $$\left. \cdots ,\alpha _n\right\} $$ ⋯ , α n as $$S_{\mathcal {B}}=\left\{ \alpha _{i}a_{i} : a_{i}\ne 0\right. $$ S B = α i a i : a i ≠ 0 and $$\left. \alpha _{i}\in \mathbb {V}\right\} $$ α i ∈ V such that $$a\sim b$$ a ∼ b if $$S_{\mathcal {B}}\left( a\right) \cup S_{\mathcal {B}}\left( b\right) =\mathcal {B}$$ S B a ∪ S B b = B . We establish some of the results about book thickness, Hamiltonian of the non-zero component union graph and also the planar, toroidal graphs with $$\dim (\Gamma \left( \mathbb {V}_{\mathcal {B}}\right) )=\frac{n}{m}$$ dim ( Γ V B ) = n m of the non-zero component union graphs of the finite dimensional vector space.

Keywords: Book thickness; Hamiltonian; Planar; Toroidal graph; 05C45; 05C10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00250-9

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