A Characterization of Trees in Which No Edge is Essential to the Domination Number

Abstract

For any tree \(T\), let \(\gamma(T)\) represent the size of a minimum dominating set. Let \({E}_0\) represent the collection of trees with the property that, regardless of the choice of edge \(e\) belonging to the tree \(T\), \(\gamma(T – e) = \gamma(T)\). We present a constructive characterization of \({E}_0\).