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Comments on “On Integral Graphs Which Belong to the Class \(\overline{\alpha K_{a,b}}\)” [Graphs Comb. 19, 527–532 (2003)]

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Abstract

Lepović gave a characterization of integral graphs of the form \(\overline{\alpha K_{a,b}}\) in “On Integral Graphs Which Belong to the Class \(\overline{\alpha K_{a,b}}\)” [Graphs Comb. 19, 527–532 (2003)]. However, for majority of the graphs \(\overline{\alpha K_{a,b}}\) declared to be integral in this result, their spectrum also includes non-integer eigenvalues \(-1\pm \sqrt{ab}\). Here we correct this result and indicate that integral graphs of this form are indeed very rare.

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Acknowledgements

D. Stevanović was supported by the research project ON174033 of the Ministry of Education, Science and Technological Development of Serbia.

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Authors and Affiliations

  1. Faculty of Education, Trnava University, Trnava, Slovakia

    Milan Pokorný

  2. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Dragan Stevanović

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  1. Milan Pokorný
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  2. Dragan Stevanović
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Correspondence to Dragan Stevanović.

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Pokorný, M., Stevanović, D. Comments on “On Integral Graphs Which Belong to the Class \(\overline{\alpha K_{a,b}}\)” [Graphs Comb. 19, 527–532 (2003)]. Graphs and Combinatorics 36, 1263–1268 (2020). https://doi.org/10.1007/s00373-020-02180-x

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  • DOI: https://doi.org/10.1007/s00373-020-02180-x

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