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

Luis Medina (), Jonnathan Rodríguez and Macarena Trigo
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Luis Medina: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Jonnathan Rodríguez: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Macarena Trigo: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2023, vol. 12, issue 1, 1-21

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.

Keywords: Harary matrix; Laplacian-energy-like; vertex connectivity; reciprocal distance Laplacian matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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