Some families of digraphs determined by the complementarity spectrum

In this paper we study seven families of digraphs, and we determine whether digraphs in these families can be determined by their spectral radius. These seven families have been characterized as the only families of digraphs with exactly three complementarity eigenvalues [1], and therefore our resul...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 709; pp. 364 - 384
Main Authors Bravo, Diego, Cubría, Florencia, Fiori, Marcelo, Rama, Gustavo
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.03.2025
Subjects
Complementarity spectrum
Digraph characterization
Spectral radius
05C20
Complementarity spectrum
Digraph characterization
05C50
05C25
Spectral radius
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Summary:In this paper we study seven families of digraphs, and we determine whether digraphs in these families can be determined by their spectral radius. These seven families have been characterized as the only families of digraphs with exactly three complementarity eigenvalues [1], and therefore our results have consequences in this context, showing which families can be determined by the complementarity spectrum. As a particular case, we prove that the θ-digraphs can be characterized by the spectral radius, extending some recent results on this family [2].
ISSN:0024-3795
DOI:10.1016/j.laa.2025.01.022