A Lower Bound for the Algebraic Connectivity of a Graph in Terms of the Domination Number

Abstract

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 $$\gamma\leq\frac{n+2}{3}$$ , and finally present a lower bound for the algebraic connectivity in terms of the domination number. We also characterize the minimum algebraic connectivity of graphs with domination number half their order.