On the spectrum of linear dependence graph of a finite dimensional vector space

In this article, we introduce and characterize linear dependence graph Γ(V) of a finite dimensional vector space V over a finite field of q elements. Two vector spaces U and V are isomorphic if and only if their linear dependence graphs Γ(U) and Γ(V) are isomorphic. The linear dependence graph Γ(V)...

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Main Authors: Maity, Sushobhan; Department of Mathematics, Visva-Bharati, Santin (Author), Bhuniya, A. K.; Department of Mathematics, Visva-Bharati, Santin (Author)
Other Authors: DST-INSPIRE, India (Fellowship grant no. DST/INSPIRE Fellowship/2014/161) (Contributor)
Format: EJournal Article
Published: GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2019-04-05.
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042 |a dc 
100 1 0 |a Maity, Sushobhan; Department of Mathematics, Visva-Bharati, Santin  |e author 
100 1 0 |a DST-INSPIRE, India   |q  (Fellowship grant no. DST/INSPIRE Fellowship/2014/161)   |e contributor 
700 1 0 |a Bhuniya, A. K.; Department of Mathematics, Visva-Bharati, Santin  |e author 
245 0 0 |a On the spectrum of linear dependence graph of a finite dimensional vector space 
260 |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,   |c 2019-04-05. 
500 |a https://www.ejgta.org/index.php/ejgta/article/view/493 
520 |a In this article, we introduce and characterize linear dependence graph Γ(V) of a finite dimensional vector space V over a finite field of q elements. Two vector spaces U and V are isomorphic if and only if their linear dependence graphs Γ(U) and Γ(V) are isomorphic. The linear dependence graph Γ(V) is Eulerian if and only if q is odd. Highly symmetric nature of Γ(V) is reflected in its automorphism group Sm ⊕ ( ⊕ i = 1mSq − 1), where m = (qn − 1)/(q − 1). Besides these basic characterizations of Γ(V), the main contribution of this article is to find eigen values of adjacency matrix, Laplacian matrix and distance matrix of this graph. 
540 |a Copyright (c) 2019 Electronic Journal of Graph Theory and Applications (EJGTA) 
546 |a eng 
690 |a graph, linear dependence, Laplacian, distance, spectrum 
655 7 |a info:eu-repo/semantics/article  |2 local 
655 7 |a info:eu-repo/semantics/publishedVersion  |2 local 
655 7 |a Peer-reviewed Article  |2 local 
786 0 |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications; 43-59 
786 0 |n 2338-2287 
787 0 |n https://www.ejgta.org/index.php/ejgta/article/view/493/pdf_94 
856 4 1 |u https://www.ejgta.org/index.php/ejgta/article/view/493/pdf_94  |z Get Fulltext