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: | , |
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| Format: | EJournal Article |
| Published: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2019-04-05.
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| Subjects: | |
| Online Access: | Get Fulltext |
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| Summary: | 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. |
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| Item Description: | https://www.ejgta.org/index.php/ejgta/article/view/493 |