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Prikladnaya Diskretnaya Matematika, 2014, Number 3(25), Pages 81–85 (Mi pdm468)  

Applied Graph Theory

On the problem of circulant networks with the maximal number of nodes for any diameter

E. A. Monakhova, O. G. Monakhov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
References:
Abstract: 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.
Document Type: Article
UDC: 519.87+519.6+519.178
Language: Russian
Citation: E. A. Monakhova, O. G. Monakhov, “On the problem of circulant networks with the maximal number of nodes for any diameter”, Prikl. Diskr. Mat., 2014, no. 3(25), 81–85
Citation in format AMSBIB
\Bibitem{MonMon14}
\by E.~A.~Monakhova, O.~G.~Monakhov
\paper On the problem of circulant networks with the maximal number of nodes for any diameter
\jour Prikl. Diskr. Mat.
\yr 2014
\issue 3(25)
\pages 81--85
\mathnet{http://mi.mathnet.ru/pdm468}
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    Прикладная дискретная математика
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