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

TL;DR

This paper establishes a lower bound for the algebraic connectivity of graphs based on their domination number, analyzing how graph modifications affect connectivity.

Contribution

It introduces a new lower bound for algebraic connectivity related to the domination number and explores graph modifications impacting this metric.

Findings

Derived a lower bound for algebraic connectivity in terms of domination number

Analyzed the effect of relocating connected branches on algebraic connectivity

Identified minimal algebraic connectivity configurations for fixed domination numbers

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 $\gamma \le \frac{n+2}{3}$, and finally present a lower bound for the algebraic connectivity in terms of the domination number.