Extremal Sombor Index of Graphs with Cut Edges and Clique Number.

The Sombor index is defined as S O (G) = ∑ u v ∈ E (G) d 2 (u) + d 2 (v) , where d (u) and d (v) represent the number of edges in the graph G connected to the vertices u and v, respectively. In this paper, we characterize the largest and second largest Sombor indexes with a given number of cut edges. Moreover, we determine the upper and lower sharp bounds of the Sombor index with a given number of clique numbers, and we characterize the extremal graphs. [ABSTRACT FROM AUTHOR]