\(H\)-forming sets in graphs
The \(H\)-forming number of a graph \(G\) is one of the modern variants of numbers concerning domination in graphs. Let \(G\) and \(H\) be graphs. An \(H\)-forming set of \(G\) is a set \(S\subseteq V(G)\) such that for each \(v\in V(G)-S\) there exists a subset \(R\) of \(S\) with \(|R|=|V(H)|-1\) and such that the subgraph induced by \(R\cup\{v\}\) contains \(H\) as subgraph. The minimum number of vertices of an \(H\)-forming set in \(G\) is the \(H\)-forming number \(\gamma_{(H)}(G)\) of \(G\). In this paper the \(H\)-forming number is studied and compared with the domination number and the total domination number. Special attention is devoted to the case that \(H\) is a path of length 2.
scientific article; zbMATH DE number 1901897
scientific article