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On Spectral Radius and Energy of a Graph with Self-Loops.
- Source :
- Mathematical Problems in Engineering; 5/10/2024, Vol. 2024, p1-7, 7p
- Publication Year :
- 2024
-
Abstract
- The spectral radius of a square matrix is the maximum among absolute values of its eigenvalues. Suppose a square matrix is nonnegative; then, by Perron–Frobenius theory, it will be one among its eigenvalues. In this paper, Perron–Frobenius theory for adjacency matrix of graph with self-loops A G S will be explored. Specifically, it discusses the nontrivial existence of Perron–Frobenius eigenvalue and eigenvector pair in the matrix A G S − σ n I , where σ denotes the number of self-loops. Also, Koolen–Moulton type bound for the energy of graph G S is explored. In addition, the existence of a graph with self-loops for every odd energy is proved. [ABSTRACT FROM AUTHOR]
- Subjects :
- NONNEGATIVE matrices
ABSOLUTE value
EIGENVALUES
BINDING energy
Subjects
Details
- Language :
- English
- ISSN :
- 1024123X
- Volume :
- 2024
- Database :
- Complementary Index
- Journal :
- Mathematical Problems in Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 177183956
- Full Text :
- https://doi.org/10.1155/2024/7056478