The article explores circulant graphs with 8 and 9 connections, focusing on extreme cases with small connections and any distance between points. By building on previous work with 6 and 7 connections, the researchers found new extreme graphs for 8 and 9 connections. These graphs set new lower limits for larger distances and are likely to be the most extreme. They proved that a solution exists for 8 connections at any distance. The researchers also suggest possible solutions for circulant graphs with even more connections.