The independence number of circulant triangle-free graphs

The independence number of circulant triangle-free graphs for 2-regular, 3-regular graphs are investigated. It is shown that the independence ratio of circulant triangle-free graphs for 3-regular graphs is at least 3/8. Some bounds for the number of vertices of r-regular circulant triangle-free graphs with independence number equal to r for odd degrees are determined. These bounds are close to Sidorenko’s bounds for even degrees.