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On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Author

Listed:
  • 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)

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.

Suggested Citation

  • Maryam Baghipur & Modjtaba Ghorbani & Hilal A. Ganie & Yilun Shang, 2021. "On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue," Mathematics, MDPI, vol. 9(5), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:512-:d:508748
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    References listed on IDEAS

    as
    1. Abdollah Alhevaz & Maryam Baghipur & Yilun Shang, 2019. "Merging the Spectral Theories of Distance Estrada and Distance Signless Laplacian Estrada Indices of Graphs," Mathematics, MDPI, vol. 7(10), pages 1-24, October.
    2. Yilun Shang, 2020. "Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs," Mathematics, MDPI, vol. 8(7), pages 1-8, July.
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    Cited by:

    1. Maryam Baghipur & Modjtaba Ghorbani & Shariefuddin Pirzada & Najaf Amraei, 2023. "On the Generalized Adjacency Spread of a Graph," Mathematics, MDPI, vol. 11(6), pages 1-9, March.
    2. Rather, Bilal A. & Ganie, Hilal A. & Shang, Yilun, 2023. "Distance Laplacian spectral ordering of sun type graphs," Applied Mathematics and Computation, Elsevier, vol. 445(C).

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