Sombor indices of graphs and their bounds

The Sombor Index (SO) is a recently introduced, intriguing topological index that has quickly garnered significant attention. Its mathematical properties and chemical applications have become the subject of numerous studies. Particularly in the field of chemical graph theory, the Sombor index is not only popular but also an actively researched area. The concept of the Sombor index has been extended to linear algebra through the definition of the Sombor matrix, which has led to intensive exploration, especially in the context of energy of matrix. The Sombor matrix is naturally associated with a graph based on the degrees of its vertices. The energy of this matrix is defined as the sum of the absolute values of its eigenvalues. This novel topological index has significantly advanced research in chemical graph theory, paving the way for the exploration of spectra and various spectrum-based features. In this thesis, the studies conducted until today with the first inclusion of the Sombor index in the literature have been compiled.