Graphs with Three Distinct α-Eigenvalues


In this paper, we investigate properties of graphs with three distinct α-eigenvalues of the matrix Aα. In particular, we show for some α the connected graph G = Kne,G = K1 ∨ (nKn) and some cones over strongly regular graph admit three distinct α-eigenvalues.

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The authors would like to thank anonymous referees for many helpful comments and suggestions to the earlier version of this paper.


This work is supported by the Joint NSFC-ISF Research Program (jointly funded by the National Natural Science Foundation of China and the Israel Science Foundation (No. 11561141001)), the National Natural Science Foundation of China (No. 11531001).

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Correspondence to Xiao-Dong Zhang.

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Tahir, M.A., Zhang, X. Graphs with Three Distinct α-Eigenvalues. Acta Math Vietnam 43, 649–659 (2018).

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  • A α matrix
  • α-eigenvalues
  • Join of graphs
  • Strongly regular graph

Mathematics Subject Classification (2010)

  • 05C50
  • 05C75