A lower bound for the algebraic connectivity of a graph in terms of the domination number

We investigate how the algebraic connectivity of a graph changes by relocating a connected branch from one vertex to another vertex, and then minimize the algebraic connectivity among all connected graphs of order $n$ with fixed domination number $\gamma \le \frac{n+2}{3}$, and finally present a lower bound for the algebraic connectivity in terms of the domination number.