Introduction to Alliances in Graphs
Petter Kristiansen, Sandra M. Hedetniemi, Stephen T. Hedetniemi · 2022
A defensive alliance in a graph G = (V,E) is a set of vertices S ⊂ V satisfying the condition that every vertex v ∈ S has at most one more neighbor in V − S than it has in S. In this paper we introduce this new concept, together with a variety of other kinds of alliances, and initiate the study of their mathematical properties.