Work

Limit points for the spectral radii of unbalanced signed graphs

Year: 2025

Type: article

Abstract: The spectral radius of a signed graph Γ = ( G , σ ) is the largest absolute value of its adjacency eigenvalues. In this paper we prove that sequences of unbalanced signed graphs suffice to retrieve all the possible limit points for the spectral radii of signed graphs. In order to achieve this result it turns out to be decisive a revisiting of the celebrated Shearer's construction of the sequence of simple (unsigned) graphs whose index tends to a fixed real number a ⩾ 2 + 5 . Additionally, our technique helps to detect infinite pairs of non-isomorphic cospectral pairs with unbalanced quadrangles.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2025.114855

Authors: Maurizio Brunetti, Vilmar Trevisan

Institutions: University of Naples Federico II, Universidade Federal do Rio Grande do Sul

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funders: Università degli Studi di Napoli Federico II, Istituto Nazionale di Alta Matematica "Francesco Severi", Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico