On the Generalized Adjacency Spread of a Graph

Article Mathematics, Applied

On the eigenvalues and spread of the generalized distance matrix of a graph

Maryam Baghipur et al.

Summary: In this paper, we study the generalized distance matrix and the generalized distance spread, and obtain upper and lower bounds for the minimum eigenvalue and the spread. We also discuss their applications and properties in graph theory.

COMPUTATIONAL & APPLIED MATHEMATICS (2022)

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Article Mathematics

Bounds for the spectral radius and energy of extended adjacency matrix of graphs

Zhao Wang et al.

Summary: The extended adjacency matrix of a graph was introduced as a precursor for developing molecular topological descriptors, with the spectral radius and extended energy successfully utilized in QSPR/QSAR investigations. The study further analyzed the mathematical properties of these descriptors, obtaining sharp upper bounds for the extended energy and presenting Nordhaus-Gaddum-type results for the spectral radius and extended energy.

LINEAR & MULTILINEAR ALGEBRA (2021)

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Article Mathematics, Applied

Some Nordhaus-Gaddum type results of Aα-eigenyalues of weighted graphs

Changxiang He et al.

Summary: The text discusses the concept of weighted graphs and their A(alpha)-matrix, as well as properties of A(alpha) eigenvalues when edge weights belong to (0,1).

APPLIED MATHEMATICS AND COMPUTATION (2021)

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Article Mathematics

On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Maryam Baghipur et al.

Summary: This study investigates upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters, characterizes all graphs attaining these new bounds, and concludes that complete graph K-n and graph K-n-e obtained from K-n by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue among all connected graphs with n vertices.

MATHEMATICS (2021)

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Article Mathematics, Applied

On the eigenvalue and energy of extended adjacency matrix

Modjtaba Ghorbani et al.

Summary: This paper investigates the extended adjacency matrix of a graph, explores its spectral properties and provides lower and upper bounds on the extended adjacency spectral radii. Additionally, the behavior of the extended adjacency energy of the graph is studied.

APPLIED MATHEMATICS AND COMPUTATION (2021)

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Article Mathematics

On the Aα-Eigenvalues of Signed Graphs

Germain Pasten et al.

Summary: This paper examines the basic properties of the matrix A(alpha)(G(σ)), including its positive semidefiniteness and some bounds on its eigenvalues, particularly deriving lower and upper bounds on its largest eigenvalue.

MATHEMATICS (2021)

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Article Mathematics, Applied