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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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2019-04-05.
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| LEADER | 02043 am a22002533u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_493_pdf_94 | ||
| 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 |