Authors: Pokorný, Milan
Stevanović, Dragan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Comments on “On Integral Graphs Which Belong to the Class αKa,b¯ ” [Graphs Comb. 19, 527–532 (2003)]
Journal: Graphs and Combinatorics
Volume: 36
First page: 1263
Last page: 1268
Issue Date: 11-May-2020
Rank: M23
ISSN: 0911-0119
DOI: 10.1007/s00373-020-02180-x
Abstract: 
Lepović gave a characterization of integral graphs of the form αKa,b¯ in “On Integral Graphs Which Belong to the Class αKa,b¯ ” [Graphs Comb. 19, 527–532 (2003)]. However, for majority of the graphs αKa,b¯ declared to be integral in this result, their spectrum also includes non-integer eigenvalues -1±ab. Here we correct this result and indicate that integral graphs of this form are indeed very rare.
Keywords: Complement of union of isomorphic complete bipartite graphs | Integral graph | Main eigenvalue
Publisher: Springer Link
Project: Graph theory and mathematical programming with applications in chemistry and computer science 

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