Acta Mathematica Vietnamica

, Volume 43, Issue 4, pp 649–659 | Cite as

Graphs with Three Distinct α-Eigenvalues

  • Muhammad Ateeq Tahir
  • Xiao-Dong ZhangEmail author


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.


Aα matrix α-eigenvalues Join of graphs Strongly regular graph 

Mathematics Subject Classification (2010)

05C50 05C75 



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

Funding information

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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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences, MOE-LSCSHL-MAC, Shanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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