A defensive alliance in a graph G=(V,E) is a set of vertices S satisfying the condition that every vertex v∈S has at least as many neighbors (including itself) in S than it has in V∖S. We also consider strong defensive alliances where the vertex itself is not considered in the inequality. We consider two notions of minimality in this paper, local and global minimality and we are interested in minimal (strong) defensive alliances of maximum size. We also look at connected versions of these alliances. We show that these problems are NP-hard.
- Defensive alliance
- Graphs of bounded average degree
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics