Changing upper irredundance by edge addition (Q1810642)

Denote the upper irredundance number of a graph \(G\) by \(\text{IR}(G)\). A graph \(G\) is IR-edge-addition-sensitive if its upper irredundance number changes whenever an edge of \(\overline G\) is added to \(G\). It is proved that if \(G\) is IR-edge-addition-sensitive then either \(\text{IR}(G+ e)< \text{IR}(G)\) for every \(e\in\overline G\) or \(\text{IR}(G+ e)> \text{IR}(G)\) for every \(e\in\overline G\).