Geodesic
On the problem of circulant networks with the maximal number of nodes for any diameter
Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 81-85.

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For undirected circulant networks, the problem of the maximal reachable number of nodes under given dimension and diameter of a graph is considered. In 1994, F. P. Muga proved the theorem that this number is odd for any dimension and any diameter of a circulant graph. Later, R. R. Lewis has presented a counterexample of four-dimensional circulant. In the present paper, a mistake in the proof of this theorem is pointed. Based on the new results, the early presented table of the maximal reachable orders of four-dimensional circulants is corrected.
Keywords: undirected circulant graphs, diameter, maximum order of a graph. 
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E. A. Monakhova; O. G. Monakhov. On the problem of circulant networks with the maximal number of nodes for any diameter. Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 81-85. http://geodesic.mathdoc.fr/item/PDM_2014_3_a6/

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