A general VDB topological index of a tree \( T \) is defined as \[ TI_f(T)=\sum_{uv\in E(T)} f(d(u),d(v)), \] where \( f(x,y) \) is a real symmetric function for \( x,y\geq 1 \). This paper aims to solve the minimum value problems of VDB indices for trees with given pendent vertices through a unified approach. We present the sufficient conditions for achieving the minimum value and characterize the extremal graphs. As an application, we demonstrate that fifteen types of VDB indices satisfy these sufficient conditions.