An upper bound on the total restrained domination number of a tree
Let \(V\) be the set of vertices in a given graph. A subset \(S\) of \(V\) is a total restrained domination set if every vertex is adjacent to a vertex in \(S\) and every vertex not in \(S\) is also adjacent to a vertex in \(V - S\). The total restrained domination number of a graph is the minimum cardinality of a total restrained domination set of the graph. A support vertex is a vertex of degree at least two which is adjacent to a leaf. The authors provide an upper bound on the total restrained domination number of a tree in terms of its order, number of leaves and number of support vertices. Finally, trees are constructively characterized attaining the established bound.
scientific article; zbMATH DE number 5815475