LAUSR

The general sum-connectivity index of a graph G is defined as $$\chi _\alpha (G)=\sum _{uv\in E(G)}(d(u)+d(v))^{\alpha }$$ χ α ( G ) = ∑ u v ∈ E ( G ) ( d ( u ) + d ( v ) ) α , where d ( u ) denotes the degree of a vertex u in G and $$\alpha $$ α is a real number. In this paper, we determine the minimum general sum-connectivity indices of trees with n vertices and matching number m , where $$n=2m$$ n = 2 m for $$\alpha \le -\,2$$ α ≤ - 2 and $$2m\le n\le 3m+1$$ 2 m ≤ n ≤ 3 m + 1 for $$\alpha >1$$ α > 1 , respectively. The corresponding extremal graphs are also characterized.