A note on graphs which have upper irredundance equal to independence
A subset \(D\) of the vertex set \(V(G)\) of a graph \(G\) is called independent, if no two vertices of \(D\) are adjacent in \(G\). A set \(I\subseteq V(G)\) is called irredundant, if for each \(x\in I\) either \(x\) is isolated, or there exists \(y\in V(G)-I\) adjacent to \(x\) and to no other vertex of \(I\). The greatest number of vertices of an independent (or irredundant) set in \(G\) is called the independence number \(\beta(G)\) (or upper irredundance number \(\text{IR}(G)\) respectively) of the graph \(G\). If \(\text{IR}(H)=\beta(H)\) for all induced subgraphs \(H\) of \(G\), then \(G\) is called irredundant perfect. These graphs are characterized. Some further results are presented concerning the upper domination number.
scientific article; zbMATH DE number 428105
scientific article