Defensive Alliances in Circulant Graphs

Abstract

In this paper we study defensive alliances in some specific regular graphs, the circulant graphs, i.e. Cayley graphs on a cyclic group.The critical defensive alliances of a circulant graph of degree at most \(6\) are completely determined. For the general case, we give tight lower and upper bounds on the alliance number of a circulant graph with \(d\) generators.