Publications Repository - Gdańsk University of Technology

A 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The non-isolating 2-bondage number of G, denoted by b_2'(G), is the minimum cardinality among all sets of edges E' subseteq E such that delta(G-E') >= 1 and gamma_2(G-E') > gamma_2(G). If for every E' subseteq E, either gamma_2(G-E') = gamma_2(G) or delta(G-E') = 0, then we define b_2'(G) = 0, and we say that G is a gamma_2-non-isolatingly strongly stable graph. First we discuss the basic properties of non-isolating 2-bondage in graphs. We find the non-isolating 2-bondage numbers for several classes of graphs. Next we show that for every non-negative integer there exists a tree having such non-isolating 2-bondage number. Finally, we characterize all gamma_2-non-isolatingly strongly stable trees.

Authors

• dr inż. Marcin Krzywkowski link open in new tab