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The A α -Spectral Radii of Graphs with Given Connectivity

Author

Listed:
  • Chunxiang Wang

    (School of Mathematics and Statistics and Hubei key Laboratory Mathematics Sciences, Central China Normal University, Wuhan 430079, China
    These authors contributed equally to this work.)

  • Shaohui Wang

    (Department of Mathematics, Savannah State University, Savannah, GA 31419, USA
    These authors contributed equally to this work.)

Abstract

The A α -matrix is A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) with α ∈ [ 0 , 1 ] , given by Nikiforov in 2017, where A ( G ) is adjacent matrix, and D ( G ) is its diagonal matrix of the degrees of a graph G . The maximal eigenvalue of A α ( G ) is said to be the A α -spectral radius of G . In this work, we determine the graphs with largest A α ( G ) -spectral radius with fixed vertex or edge connectivity. In addition, related extremal graphs are characterized and equations satisfying A α ( G ) -spectral radius are proposed.

Suggested Citation

  • Chunxiang Wang & Shaohui Wang, 2019. "The A α -Spectral Radii of Graphs with Given Connectivity," Mathematics, MDPI, vol. 7(1), pages 1-6, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:44-:d:194975
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