Publications Repository - Gdańsk University of Technology

A total outer-independent dominating set of a graph G=(V(G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have gamma_t^{oi}(T) >= (2n+s-l)/3, and we characterize the trees attaining this upper bound.

Authors

• dr inż. Marcin Krzywkowski link open in new tab