Graphs with Three Distinct α-Eigenvalues

Abstract

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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Acknowledgements

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

Funding

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). https://doi.org/10.1007/s40306-018-0275-y

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Keywords

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

Mathematics Subject Classification (2010)

  • 05C50
  • 05C75