Coronae Graphs and Their \(\alpha \)-Eigenvalues

Abstract

Let \(G_1\) and \(G_2\) be two simple connected graphs. The properties of \(\alpha -\)eigenvalues of four coronal graphs of \(G_1\) and \(G_2\): \(G_1 \circ G_2, G_1\lozenge G_2\), \(G_1 \odot G_2\) and \(G_1 \circleddash G_2\) have been studied. As an application, we construct infinitely many pairs of non-isomorphic graphs with the same \(\alpha \)-eigenvalues.

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Acknowledgements

The authors would like to thank the anonymous referees for careful reading and suggestions to an earlier version of this paper, which results in an improvement.

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Correspondence to Xiao-Dong Zhang.

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This work is supported by the National Natural Science Foundation of China (Nos.11971311 and 11531001), the Montenegrin-Chinese Science and Technology Cooperation Project (No.3-12) and the Joint NSFC-ISF Research Program (jointly funded by the National Natural Science Foundation of China and the Israel Science Foundation (No. 11561141001)).

Communicated by Sanming Zhou.

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Tahir, M.A., Zhang, X. Coronae Graphs and Their \(\alpha \)-Eigenvalues. Bull. Malays. Math. Sci. Soc. 43, 2911–2927 (2020). https://doi.org/10.1007/s40840-019-00845-2

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Keywords

  • \(\alpha \)-Eigenvalue
  • Corona
  • Edge corona
  • R-vertex corona
  • R-edge corona
  • Isospectral graph

Mathematics Subject Classification

  • 05C50
  • 05C76