A circulant graph is a graph of n graph vertices in which the ith graph vertex is adjacent to the (i + j)th and (i - j)th graph vertices for each j in a list l. The circulant graph Ci_n(1, 2, ..., ⌊n/2⌋) gives the complete graph K_n and the graph Ci_n(1) gives the cyclic graph C_n. The circulant graph on n vertices on an offset list l is implemented in the Wolfram Language as CirculantGraph[n, l]. Precomputed properties are available using GraphData[{Circulant, {n, l}}]. With the exception of the degenerate case of the path graph P_2, connected circulant graphs are biconnected, bridgeless, cyclic, Hamiltonian, LCF, regular, traceable, and vertex-transitive.

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