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The diameter of a graph is the maximum distance among all pairs of vertices.Thus a graph $G$ has diameter $d$ if any two vertices are at distance at most$d$ and there are two vertices at distance $d$. We are interested in studyingthe diameter of circulant graphs $C_n(1,s)$, i.e., graphs with the set$\{0,1,\ldots, n-1\}$ of integers as vertex set and in which two distinctvertices $i,j \in \{0,1,\ldots, n-1\}$ are adjacent if and only if $|i-j|_n\in\{1,s\}$, where $2\leq s\leq \lfloor \frac{n-1}{2} \rfloor$ and$|x|_n=\min(|x|, n-|x|)$. Despite the regularity of circulant graphs, it isdifficult to evaluate several parameters, in particular the distance and thediameter. To the best of our knowledge, there is no formulas providing exactvalues for the distance and the diameter of $C_n(1,s)$ for all $n$ and $s$. Inthis context, we present in this paper a new approach, based on a simplealgorithm, that gives exact values for the distance and the diameter ofcirculant graphs.

A new approach for computing the distance and the diameter in circulant graphs