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New Spectral Results for Laplacian Harary Matrix and the Harary Laplacian-Energy-like Applying a Matrix Order Reduction

Author

Listed:
  • Luis Medina

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Jonnathan Rodríguez

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Macarena Trigo

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

Abstract

In this paper, we introduce the concepts of Harary Laplacian-energy-like for a simple undirected and connected graph G with order n . We also establish novel matrix results in this regard. Furthermore, by employing matrix order reduction techniques, we derive upper and lower bounds utilizing existing graph invariants and vertex connectivity. Finally, we characterize the graphs that achieve the aforementioned bounds by considering the generalized join operation of graphs.

Suggested Citation

  • Luis Medina & Jonnathan Rodríguez & Macarena Trigo, 2023. "New Spectral Results for Laplacian Harary Matrix and the Harary Laplacian-Energy-like Applying a Matrix Order Reduction," Mathematics, MDPI, vol. 12(1), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:2-:d:1302913
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