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Upper and Lower Bounds for the Spectral Radius of Generalized Reciprocal Distance Matrix of a Graph

Author

Listed:
  • Yuzheng Ma

    (School of Data Science and Technology, North University of China, Taiyuan 030051, China)

  • Yubin Gao

    (School of Mathematical Sciences, North University of China, Taiyuan 030051, China)

  • Yanling Shao

    (School of Mathematical Sciences, North University of China, Taiyuan 030051, China)

Abstract

For a connected graph G on n vertices, recall that the reciprocal distance signless Laplacian matrix of G is defined to be R Q ( G ) = R T ( G ) + R D ( G ) , where R D ( G ) is the reciprocal distance matrix, R T ( G ) = d i a g ( R T 1 , R T 2 , ⋯ , R T n ) and R T i is the reciprocal distance degree of vertex v i . In 2022, generalized reciprocal distance matrix, which is defined by R D α ( G ) = α R T ( G ) + ( 1 − α ) R D ( G ) , α ∈ [ 0 , 1 ] , was introduced. In this paper, we give some bounds on the spectral radius of R D α ( G ) and characterize its extremal graph. In addition, we also give the generalized reciprocal distance spectral radius of line graph L ( G ) .

Suggested Citation

  • Yuzheng Ma & Yubin Gao & Yanling Shao, 2022. "Upper and Lower Bounds for the Spectral Radius of Generalized Reciprocal Distance Matrix of a Graph," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2683-:d:875620
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    Cited by:

    1. Irina Cristea & Hashem Bordbar, 2023. "Preface to the Special Issue “Algebraic Structures and Graph Theory”," Mathematics, MDPI, vol. 11(15), pages 1-4, July.

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