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Generalized Randić Estrada Indices of Graphs

Author

Listed:
  • Eber Lenes

    (Área de Ciencias Básicas Exactas, Grupo de Investigación Deartica, Universidad del Sinú, Cartagena 130001, Colombia
    These authors contributed equally to this work.)

  • Exequiel Mallea-Zepeda

    (Departamento de Matemática, Universidad de Tarapacá, Arica 1000000, Chile
    These authors contributed equally to this work.)

  • Luis Medina

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

  • Jonnathan Rodríguez

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

Abstract

Let G be a simple undirected graph on n vertices. V. Nikiforov studied hybrids of A G and D G and defined the matrix A α G for every real α ∈ [ 0 , 1 ] as A α G = α D G + ( 1 − α ) A G . In this paper, we define the generalized Randić matrix for graph G , and we introduce and establish bounds for the Estrada index of this new matrix. Furthermore, we find the smallest value of α for which the generalized Randić matrix is positive semidefinite. Finally, we present the solution to the problem proposed by V. Nikiforov. The problem consists of the following: for a given simple undirected graph G , determine the smallest value of α for which A α G is positive semidefinite.

Suggested Citation

  • Eber Lenes & Exequiel Mallea-Zepeda & Luis Medina & Jonnathan Rodríguez, 2022. "Generalized Randić Estrada Indices of Graphs," Mathematics, MDPI, vol. 10(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2932-:d:888105
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