1. On the A α -Eigenvalues of Signed Graphs.
- Author
-
Pastén, Germain, Rojo, Oscar, and Medina, Luis
- Subjects
- *
UNDIRECTED graphs , *EIGENVALUES - Abstract
For α ∈ [ 0 , 1 ] , let A α (G σ) = α D (G) + (1 − α) A (G σ) , where G is a simple undirected graph, D (G) is the diagonal matrix of its vertex degrees and A (G σ) is the adjacency matrix of the signed graph G σ whose underlying graph is G. In this paper, basic properties of A α (G σ) 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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF