The smallest sum-connectivity index on trees with n vertices and k pendant vertices

For a given connected graph G and a real number α , denote by d ( u ) the degree of vertex u of G , and denote by χ α ( G ) = ∑ u v ∈ E ( G ) ( d ( u ) + d ( v ) ) α the general sum-connectivity index of G . In the present note, we determine the smallest general sum-connectivity index of trees (resp., chemical trees) together with corresponding extremal trees among all trees (resp., chemical trees) with n vertices and k pendant vertices for 0 < α < 1.