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 $E_0$.