Efficient domination in circulant graphs with two chord lengths

Domination is an important property in the design of efficient computer interconnection networks. We provide a complete characterization of circulant graphs with two chord lengths that admit an efficient dominating set. In particular, for 3-regular and 4-regular circulant graphs, we give necessary and sufficient conditions for the existence of efficient dominating sets and we describe their exact structure according to the relationship between chords.