The line neighbourhood number of a graph (Q1080431)

The line neighbourhood number \(n_ 0'(G)\) of a graph G is a certain analogy of the domination number. It is defined as the minimum number of edges of a subset of the edge set of G with the property that each vertex of G is adjacent to the end vertex of some edge of this set. The number \(n_ 0'(G)\) is determined for some types of graphs (complete graphs, paths, circuits, wheels). Further it is related to various numerical invariants of the graph (vertex and edge covering numbers, vertex and edge independence numbers, vertex and edge domination numbers).