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Unbalanced unicyclic and bicyclic graphs with extremal spectral radius

Francesco Belardo;  Maurizio Brunetti;  Adriana Ciampella — 2021

Czechoslovak Mathematical Journal

A signed graph Γ is a graph whose edges are labeled by signs. If Γ has n vertices, its spectral radius is the number ρ ( Γ ) : = max { | λ i ( Γ ) | : 1 ≤ i ≤ n } , where λ 1 ( Γ ) ≥ ⋯ ≥ λ n ( Γ ) are the eigenvalues of the signed adjacency matrix A ( Γ ) . Here we determine the signed graphs achieving the minimal or the maximal spectral radius in the classes 𝔘 n and 𝔅 n of unbalanced unicyclic graphs and unbalanced bicyclic graphs, respectively.

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