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Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy

Author

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  • Luis Medina

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Av Angamos 601, Antofagasta 1240000, Chile
    All authors contributed equally to this work.)

  • Jonnathan Rodríguez

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Av Angamos 601, Antofagasta 1240000, Chile
    All authors contributed equally to this work.)

  • Macarena Trigo

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Av Angamos 601, Antofagasta 1240000, Chile
    All authors contributed equally to this work.)

Abstract

Let X be a partitioned matrix and let B its equitable quotient matrix. Consider a simple, undirected, connected graph G of order n . In this paper, we employ a technique based on quotient matrices derived from block-partitioned structures to establish new spectral results for the reciprocal distance signless Laplacian matrix. In particular, we identify a sequence of graphs whose eigenvalues are all integers. Furthermore, we introduce the concept of Harary incidence energy and extend known incidence energy results to the setting of the reciprocal distance signless Laplacian matrix. Finally, we characterize the Harary incidence energy of extremal graphs by examining vertex connectivity through the generalized graph join operation.

Suggested Citation

  • Luis Medina & Jonnathan Rodríguez & Macarena Trigo, 2025. "Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy," Mathematics, MDPI, vol. 13(17), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2720-:d:1731394
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