On nonzero component graph of vector spaces over finite fields

Das, Angsuman

doi:10.1142/s0219498817500074

Cited by 44 publications

(16 citation statements)

References 18 publications

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“…In this section, we find the degree of each vertices of Γ(V) if the base field is finite. For more results, in the case of finite fields, please refer to [9].…”

Section: The Case Of Finite Fieldsmentioning

confidence: 99%

Non-zero component union graph of a finite-dimensional vector space

Das

2016

Linear and Multilinear Algebra

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In this paper, we introduce a graph structure, called non-zero component graph on finite dimensional vector spaces. We show that the graph is connected and find its domination number and independence number. We also study the inter-relationship between vector space isomorphisms and graph isomorphisms and it is shown that two graphs are isomorphic if and only if the corresponding vector spaces are so. Finally, we determine the degree of each vertex in case the base field is finite.

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“…In this section, we find the degree of each vertices of Γ(V) if the base field is finite. For more results, in the case of finite fields, please refer to [9].…”

Section: The Case Of Finite Fieldsmentioning

confidence: 99%

Non-zero component union graph of a finite-dimensional vector space

Das

2016

Linear and Multilinear Algebra

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“…In programming, linear algebra is usually used to initialize something with algebraic variables (Phothilimthana et al, 2019). On the chart, the study of graphs related to various algebraic structures begins by introducing the idea of graphing the zero divisor of the commutative ring of unity (Das, 2017). In addition, graph theory also helps to characterize various algebraic structures by means of studying certain graphs associated to them (Das, 2016b;Dörfler et al, 2018;Sanderson et al, 2019;Zhang and Chen, 2018).…”

Section: Introductionmentioning

confidence: 99%

Detecting Similarities in Posts Using Vector Space and Matrix

Haq

2020

ijgor

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This study discusses the application of two linear algebraic materials, namely vector and matrix spaces. The application of the two materials is related to an article, the writing can be in the form of an article, book, and so on. The writings examined in this study use example sentences made by the author. Two materials of linear algebra, namely the vector space and the matrix are used to analyze whether there is a similarity between the writing made with other writing. As a result, vector space and matrix can be used to detect similarities in a text.

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“…This new technique of studying algebraic structures leads to many fascinating results and questions. For various constructions of graphs on different algebras we refer to [2,7] on rings, [3,5] on groups, [6] on semigroups, [23,24,26,33] on posets, [9,10,11,12] on vector spaces.…”

Section: Introductionmentioning

confidence: 99%

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

Maity

Bhuniya

2019

ejgta

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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 S m ⊕ (⊕ m i=1 S q−1), where m = q n −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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On nonzero component graph of vector spaces over finite fields

Cited by 44 publications

References 18 publications

Non-zero component union graph of a finite-dimensional vector space

Non-zero component union graph of a finite-dimensional vector space

Detecting Similarities in Posts Using Vector Space and Matrix

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

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