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 is an element of & Ropf;, the general Sombor index for a graph H is SOc,g(H) = & sum;(vw is an element of 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 SOc,g for c >= 1 and g > 0, trees of given order with the smallest SOc,g for c >= 1 and g >= 1, bipartite graphs of prescribed matching number and order with the largest SOc,g for c >= 1 and g >= 0 are presented. We also obtain several corollaries including bounds for the classical Sombor index and forgotten index.