Menu
For \(\pi\) one of the upper domination parameters \(\beta\), \(\Gamma\), or \(IR\), we investigate graphs for which \(\pi\) decreases ( \(\pi\)-edge-critical graphs) and graphs for which \(\pi\) increases ( \(\pi^+\)-edge-critical graphs) whenever an edge is added. We find characterisations of \(\beta\)- and \(\Gamma\)-edge-critical graphs and show that a graph is \(IR\)-edge-critical if and only if it is \(\Gamma\)-edge-critical. We also exhibit a class of \(\Gamma^+\)-edge-critical graphs.