Independant domination number of a graph

If all vertices of G belong to the set D , then the graph G has two vertices. Dominating sets are closely related to independent sets : an independent set is also a dominating set if and only if it is a maximal independent set , so any maximal independent set in a graph is necessarily also a minimal dominating set. For a comprehensive survey of domination in graphs, see [ 10 ]. Thank you, Robert Cartaino. Now assume that u is adjacent to a pendant vertex, say x. We have the following bounds on the 2-outer-independent domination number of a graph in terms of its order and size.

Main article: Interval scheduling. Maximum set packing. Categories : Graph theory objects NP-complete problems Computational problems in graph theory. Tarjan, R. Despite the close relationship between maximum cliques and maximum independent sets in arbitrary graphs, the independent set and clique problems may be very different when restricted to special classes of graphs. Chan, T. The maximum independent set problem is NP-hard.

They are independent line sets. Namespaces Article Talk. The problem of finding a maximal independent set can be solved in polynomial time by a trivial greedy algorithm. Hence these two subsets are considered as the maximal independent line sets.