Bondage number of planar graphs
A subset \(S\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). The minimum number of vertices of a dominating set in \(G\) is the domination number \(\gamma(G)\) of \(G\). The minimum number of vertices whose deletion from \(G\) changes the value of \(\gamma(G)\) for a higher one, is the bondage number \(b(G)\) of \(G\). This number is studied for planar graphs in general and in particular for graphs with forbidden minor \(K_4\).
scientific article; zbMATH DE number 1506827