Publications Repository - Gdańsk University of Technology

A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)D is independent. The double outer-independent domination number of a graph G, denoted by gamma_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We prove that for every nontrivial tree T of order n, with l leaves and s support vertices we have gamma_d^{oi}(T) >= (2n+l-s+2)/3, and we characterize the trees attaining this lower bound. We also give a constructive characterization of trees T such that gamma_d^{oi}(T) = (2n+2)/3.

Authors

• dr inż. Marcin Krzywkowski link open in new tab