Defensive alliances in regular graphs and circulant graphs
نویسندگان
چکیده
In this paper we study defensive alliances in some regular graphs. We determine which subgraphs could a critical defensive alliance of a graph G induce, if G is 6-regular and the cardinality of the alliance is at most 8. In particular, we study the case of 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.
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