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

Das, Angsuman

doi:10.1080/03081087.2016.1234577

Cited by 41 publications

(39 citation statements)

References 14 publications

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“…Firstly, we recall the definition of Non-zero Component graph of a finite dimensional vector space and some preliminary results from [9].…”

Section: Definitions and Some Basic Resultsmentioning

confidence: 99%

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On nonzero component graph of vector spaces over finite fields

Das

2017

J. Algebra Appl.

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In this paper, we study nonzero component graph Γ(V) of a finite-dimensional vector space V over a finite field F. We show that the graph is Hamiltonian and not Eulerian. We also characterize the maximal cliques in Γ(V) and show that there exists two classes of maximal cliques in Γ(V). We also find the exact clique number of Γ(V) for some particular cases. Moreover, we provide some results on size, edge-connectivity and chromatic number of Γ(V).

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“…Firstly, we recall the definition of Non-zero Component graph of a finite dimensional vector space and some preliminary results from [9].…”

Section: Definitions and Some Basic Resultsmentioning

confidence: 99%

“…Theorem 3.4. [9] Let V be a vector space over a finite field F with q elements and Γ be its associated graph with respect to a basis {α 1 , α 2 , . .…”

Section: Definitions and Some Basic Resultsmentioning

confidence: 99%

On nonzero component graph of vector spaces over finite fields

Das

2017

J. Algebra Appl.

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“…their exists at least one α i along which both v 1 and v 2 have non-zero components. Unless otherwise mention, we take the basis α α α … { , , , } n 1 2 on which the graph is constructed (Das, 2016). Now, we state some basic results about Γ( ) , which will be useful in the sequel.…”

Section: Graph Associated To a Vector Spacementioning

confidence: 99%

Eccentric topological properties of a graph associated to a finite dimensional vector space

Liu

Khalid

Rahim

et al. 2020

Main Group Metal Chemistry

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A topological index is actually designed by transforming a chemical structure into a number. Topological index is a graph invariant which characterizes the topology of the graph and remains invariant under graph automorphism. Eccentricity based topological indices are of great importance and play a vital role in chemical graph theory. In this article, we consider a graph (non-zero component graph) associated to a finite dimensional vector space over a finite filed in the context of the following eleven eccentricity based topological indices: total eccentricity index; average eccentricity index; eccentric connectivity index; eccentric distance sum index; adjacent distance sum index; connective eccentricity index; geometric arithmetic index; atom bond connectivity index; and three versions of Zagreb indices. Relationship of the investigated indices and their dependency with respect to the involved parameters are also visualized by evaluating them numerically and by plotting their results.

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

Cited by 41 publications

References 14 publications

On nonzero component graph of vector spaces over finite fields

On nonzero component graph of vector spaces over finite fields

Eccentric topological properties of a graph associated to a finite dimensional vector space

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

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