Abstract
Gutman proposed a topological index called the Sombor index, which was defined as [Formula: see text] where [Formula: see text] is the degree of the vertex [Formula: see text] in graph [Formula: see text]. In this paper, we determine the second-minimum and second-maximum values of the Sombor index over all the unicyclic graphs of order [Formula: see text] and bicyclic graphs of order [Formula: see text].
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