Sharp Bounds on the Spectral Radius and Energy of Arithmetic–Geometric Matrix
Abstract
Let Z be a graph of order n with m edges. Let Aag(Z) represents the arithmetic–geometric matrix of Z. The eigenvalues of the matrix Aag(Z) are called the arithmetic–geometric eigenvalues, and the eigenvalue with the largest modulus is called the arithmetic–geometric spectral radius of Z. The sum of the absolute values of the arithmetic–geometric eigenvalues is called the arithmetic–geometric energy of Z. In this paper, we establish sharp upper and lower bounds for the AM-GM spectral radius in terms of various graph parameters and provide a complete characterization of the extremal graphs that attain these bounds. Additionally, we derive new bounds for the AM-GM energy of a graph and identify the corresponding extremal structures. In both contexts, our results significantly improve upon several existing bounds reported in the literature.
Fields of Study & Subjects
Graph theory and applications
Matrix Theory and Algorithms
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Mathematics
- Publisher
- MDPI AG
- Volume
- 14
- Issue
- 2
- Pages
- 321–321
- Publication date
- 17 January 2026
- Language
- EN