On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Maryam Baghipur, Modjtaba Ghorbani, Hilal A. Ganie and Yilun Shang
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Maryam Baghipur: Department of Mathematics, Faculty of Science, Shahid Rajaee, Teacher Training University, Tehran 16785-136, Iran
Modjtaba Ghorbani: Department of Mathematics, Faculty of Science, Shahid Rajaee, Teacher Training University, Tehran 16785-136, Iran
Hilal A. Ganie: Department of School Education, Jammu and Kashmir Government, Kashmir 193404, India
Yilun Shang: Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK

Mathematics, 2021, vol. 9, issue 5, 1-12

Abstract: The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as R Q ( G ) = diag ( R H ( G ) ) + R D ( G ) . Here, R D ( G ) is the Harary matrix (also called reciprocal distance matrix) while diag ( R H ( G ) ) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph K n and the graph K n ? e obtained from K n by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

Keywords: signless Laplacian reciprocal distance matrix (spectrum); spectral radius; total reciprocal distance vertex; Harary matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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