On the A ? -Eigenvalues of Signed Graphs

Germain Pastén, Oscar Rojo and Luis Medina
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Germain Pastén: Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta 1240000, Chile
Oscar Rojo: Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta 1240000, Chile
Luis Medina: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2021, vol. 9, issue 16, 1-14

Abstract: For ? ? [ 0 , 1 ] , let A ? ( G ? ) = ? D ( G ) + ( 1 ? ? ) A ( G ? ) , where G is a simple undirected graph, D ( G ) is the diagonal matrix of its vertex degrees and A ( G ? ) is the adjacency matrix of the signed graph G ? whose underlying graph is G . In this paper, basic properties of A ? ( G ? ) are obtained, its positive semidefiniteness is studied and some bounds on its eigenvalues are derived—in particular, lower and upper bounds on its largest eigenvalue are obtained.

Keywords: signed graph; adjacency matrix; balanced signed graph; switching equivalent graphs; eigenvalue bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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