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- Title
On Spectral Radius and Energy of a Graph with Self-Loops.
- Authors
Vivek Anchan, Deekshitha; H. J., Gowtham; D'Souza, Sabitha
- 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.
- Subjects
NONNEGATIVE matrices; ABSOLUTE value; EIGENVALUES; BINDING energy
- Publication
Mathematical Problems in Engineering, 2024, Vol 2024, p1
- ISSN
1024-123X
- Publication type
Article
- DOI
10.1155/2024/7056478