Eigenvalues of Adjacency and Laplacian Matrices of Bracelet—K_n Graph Article Swipe

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E R Albirri , Arif Fatahillah , S Hussen , Kiki Ariyanti Sugeng ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1088/1742-6596/1839/1/012038

Let G be an undirected simple graph. Adjacency matrix of a graph G , denoted by ( A ( G )), is defined as a matrix which has entry-( i , j ) is equal 1 if vertex i and vertex j are adjacent and 0 if otherwise. Let D ( G ) be the diagonal matrix of vertex degree and J ( G ) be the matrix which has entry all ones. Laplacian matrix ( L ( G )) can be defined by L ( G ) = D ( G ) – A ( G ). This study discusses eigenvalues of adjacency and Laplacian matrices of the Bracelet— K n graph. The results of this study indicate that the Bracelet— K n graph for n ≥ 4, n even has four different eigenvalues of adjacency and Laplacian matrices.

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Combinatorics

Mathematics

Vertex (Graph Theory)

Mathematical Analysis

Geometry

Quantum Mechanics

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Adjacency matrix Combinatorics Graph energy Degree matrix Eigenvalues and eigenvectors Mathematics Laplacian matrix Vertex (graph theory) Adjacency list Diagonal matrix Laplace operator Graph Regular graph Diagonal Discrete mathematics Graph power Physics Line graph Mathematical analysis Geometry Quantum mechanics

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Language: en
Landing Page: https://doi.org/10.1088/1742-6596/1839/1/012038
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Title: Eigenvalues of Adjacency and Laplacian Matrices of Bracelet—K_n Graph

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Authors: E R Albirri, Arif Fatahillah, S Hussen, Kiki Ariyanti Sugeng

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Concepts: Adjacency matrix, Combinatorics, Graph energy, Degree matrix, Eigenvalues and eigenvectors, Mathematics, Laplacian matrix, Vertex (graph theory), Adjacency list, Diagonal matrix, Laplace operator, Graph, Regular graph, Diagonal, Discrete mathematics, Graph power, Physics, Line graph, Mathematical analysis, Geometry, Quantum mechanics

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abstract_inverted_index.study	100, 118
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abstract_inverted_index.degree	60
abstract_inverted_index.graph.	7, 113
abstract_inverted_index.matrix	9, 26, 57, 68, 75
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abstract_inverted_index.diagonal	56
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abstract_inverted_index.matrices	107
abstract_inverted_index.Adjacency	8
abstract_inverted_index.Laplacian	74, 106, 139
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abstract_inverted_index.different	134
abstract_inverted_index.discusses	101
abstract_inverted_index.matrices.	140
abstract_inverted_index.otherwise.	48
abstract_inverted_index.undirected	5
abstract_inverted_index.Bracelet—	110, 122
abstract_inverted_index.eigenvalues	102, 135
cited_by_percentile_year
countries_distinct_count	1
institutions_distinct_count	4
citation_normalized_percentile.value	0.1057266
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False

Eigenvalues of Adjacency and Laplacian Matrices of Bracelet—Kn Graph Article Swipe

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Eigenvalues of Adjacency and Laplacian Matrices of Bracelet—K_n Graph Article Swipe