On spectrum of Sombor matrix and Sombor energy of graphs

The Sombor index (SO) is a recently introduced degree-based graph invariant, defined as the sum over all pairs of adjacent vertices u, v of the term du2+d2v, where d_u and dv denote the degrees of vertices u and v, respectively. The matrix associated with SO is the Sombor matrix, and its spectrum is the Sombor spectrum. In this paper, the connected graphs having exactly two and exactly three Sombor eigenvalues are characterized. Bounds are obtained for the spectral radius and energy of the Sombor matrix, and the corresponding extremal graphs are determined. In addition, the Sombor spectra of several families of graphs are calculated.