General Sombor index of graphs and trees

Topological indices such as the general Sombor index are studied because of their extensive applications. For c, g ∈ ℝ, the general Sombor index for a graph H is SO_c,g (H) = ∑_vw∈E(H) ([d_H (v)]^c +[d_H (w)^c])^g, where E(H) is the set of edges of H, and d_H (v) and d_H (w) are the degrees of vertices v and w. Trees of given order with the largest SO_c,g for c ≥ 1 and g > 0, trees of given order with the smallest SO_c,g for c ≥ 1 and g ≥ 1, bipartite graphs of prescribed matching number and order with the largest SO_c,g for c ≥ 1 and g ≥ 0 are presented. We also obtain several corollaries including bounds for the classical Sombor index and forgotten index.