Work

A connection between the Aα-spectrum and Lovász theta number

Year: 2025

Type: article

Abstract: We show that the smallest α so that α D + ( 1 − α ) A ≽ 0 is at least 1 / ϑ ( G ‾ ) , significantly improving upon a result due to Nikiforov and Rojo (2017). In fact, we display a stronger connection: if the nonzero entries of A are allowed to vary and those of D vary accordingly, then we show that this smallest α is in fact equal to 1 / ϑ ( G ‾ ) . We also show other results obtained as an application of this optimization framework, including a connection to the well-known quadratic formulation for ω ( G ) due to Motzkin and Straus (1964).

Source: Linear Algebra and its Applications

DOI: 10.1016/j.laa.2025.04.007

Authors: Gabriel Coutinho, Thiago Oliveira

Institutions: Universidade Federal de Minas Gerais, Universidade de São Paulo

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,230

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa do Estado de Minas Gerais