Upper and Lower Bounds for the Spectral Radius of Generalized Reciprocal Distance Matrix of a Graph

Article Mathematics, Applied

Upper bounds and lower bounds for the spectral radius of Reciprocal Distance, Reciprocal Distance Laplacian and Reciprocal Distance signless Laplacian matrices

Luis Medina et al.

Summary: The Harary matrix, Reciprocal Distance Laplacian matrix, and Reciprocal Distance signless Laplacian matrix are defined for simple undirected connected graphs by different researchers in different years. This study focuses on finding upper bounds and lower bounds for the spectral radius of these matrices.

LINEAR ALGEBRA AND ITS APPLICATIONS (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

On eigenvalues of the reciprocal distance signless Laplacian matrix of graphs

Abdollah Alhevaz et al.

Summary: The paper investigates the reciprocal distance signless Laplacian matrix of a connected graph, exploring its spectral properties and constructing equienergetic graphs using specific methods. Bounds on the spectral radius of the matrix are obtained, and extremal graphs are characterized.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS (2021)

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Article Mathematics