This article is cited in 2 papers

A new attainable lower bound on the number of nodes in quadruple circulant networks

E. A. Monakhova

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia

Abstract: We consider the problem of maximization of the number of nodes for fixed degree and diameter of undirected circulant networks. The known lower bound on the maximum order of quadruple circulant networks is improved by $O(d^3)$ for any even diameter $d\equiv0\pmod4$. The family of circulant networks achieving the obtained estimate is found. As we conjecture, the found graphs are the largest circulants for the dimension four. Tab. 2, bibliogr. 9.

Keywords: undirected circulant network, diameter, maximum order of a graph.

UDC: 519.87

Received: 23.04.2012
Revised: 21.09.2012

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