A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs

In the present study, we focus on circulant graphs, Cn(S), with set of vertices {0,1,…,n−1} and in which two distinct vertices i and j are adjacent if and only if |i−j|n∈S, where S is a generating set. Despite their regularity, there are currently no established formulas to accurately determine the distance and the diameter of circulant graphs. In light of this context, we present in this paper a novel approach, which relies on a simple algorithm, capable of yielding formulas for the distance and the diameter of circulant graphs without implementing any graph.