Gutman proposed a new alternative interpretation of vertex-degree-based topological index, called Sombor index. It is defined via the term $$, where dG(vi) is the degree of the vertex vi in graph G. Deng et al. [Int. J. Quantum Chem. 121(11) (2021), e26622] proposed the following two problems: to determine the maximum value of the (reduced) Sombor index among all molecular graphs of order n and to determine the extremal (minimum and maximum) of the (reduced) Sombor index among all connected graphs with n vertices and m edges. In this paper, we solve these two problems. KEYWORDS: Degree; Sombor index; Molecular tree AMS SUBJECT CLASSIFICATION 2010: 05C05, 05C12, 05C35