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

Abstract

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 χα(G) = ∑uv∈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.