Domination on Circulant Graphs with two chord length

In this paper we present a method to find the minimum dominating set and domination number of some specific Circulant graphs Circ(n,{1, 5}). In this method we construct a tree in which each path from root to the leaf is a dominating set. At each level we compare the number of vertices dominated by the vertices in each path and select the paths which dominate the maximum number of vertices. Since this tree exhibits repeated patterns the number of comparisons are considerably reduced. Finally we arrive at a sequence (path) which gives the minimum dominating set of the Circulant graph. We also discuss the possibility of extending this methodology to Circ(n,{1, m}), where m is any positive integer greater than or equal to 6.