Fig. 2

Examples of the block-circulant graphs for different values of F and ξ, with G fixed. The figure on the top represents the case \(\mathcal {BC}_{3,10} (4,5,5 )\), obtained for \(F=3\), \(G=10\), and \(\xi_{0}=\xi_{1}=\xi_{2}=2\). The figure at the bottom shows some examples of the special case \(\operatorname{Ci}_{N} (1,2,\ldots,\xi )=\mathcal {BC}_{1,N} (2\xi -H (\xi- \lfloor\frac{N}{2} \rfloor+ (-1 )^{N} ) )\) (circulant graph) for \(N=10\), namely \(C_{N}=\operatorname {Ci}_{N} (1 )\) (cyclic graph), \(\operatorname{Ci}_{N} (1,2 )\), and finally \(K_{N}=\operatorname{Ci}_{N} (1,2,\ldots, \lfloor\frac {N}{2} \rfloor )\) (complete graph)