Some properties of the circulant graphs

In this article, we compute the diameter and Wiener index of circulant graphs. We derive a formula for the Wiener index of these graphs, which is given by two forms, depending on the integer l. Furthermore, we explore the diameter of these circulant graphs and prove that diameter is equal 2. Additionally, we establish that the circulant graph exhibits Eulerian properties when the integer l is an odd number. Our finding contribute to the understanding of the structural characteristics and metrics of circulant graphs, providing valuable insights for graph theory and related fields.