Spectrum and energy of the Sombor matrix

• Main Author: Ivan Gutman
• Format: Article
• Language: English
• Published: University of Defence in Belgrade 2021-07-01
• Series: Vojnotehnički Glasnik
• Subjects: sombor matrix; sombor energy; sombor index; vertexdegree-based graph invariant; spectrum (of matrix)
• Online Access: https://scindeks-clanci.ceon.rs/data/pdf/0042-8469/2021/0042-84692103551G.pdf

Introduction/purpose: The Sombor matrix is a vertex-degree-based matrix associated with the Sombor index. The paper is concerned with the spectral properties of the Sombor matrix. Results: Equalities and inequalities for the eigenvalues of the Sombor matrix are obtained, from which two fundamental bounds for the Sombor energy (= energy of the Sombor matrix) are established. These bounds depend on the Sombor index and on the „forgotten“ topological index. Conclusion: The results of the paper contribute to the spectral theory of the Sombor matrix, as well as to the general spectral theory of matrices associated with vertex-degree-based graph invariants.