EN|RU Volume 17, No 5, 2010, P. 56-66 UDC 519.87 E. A. Monakhova Multiplicative circulant networks Abstract: We consider the problem of maximization of the number of nodes for the given degree and diameter of circulant networks. Study of the class of multiplicative circulant networks in which the chord lengths are the powers of an odd number makes it possible to obtain new improved lower estimates of the number of nodes of circulant networks for any dimension $k \ge 4$. The infinite families of circulant networks attaining the found bounds are constructed. Bibliogr. 13. Keywords: circulant network, diameter, maximal order of a graph. Monakhova Emilia Anatol’evna 1 1. Institute of Computanional Technologies, 6 Acad. Lavrent’ev ave., 630090 Novosibirsk, Russia e-mail: emilia@rav.sscc.ru © Sobolev Institute of Mathematics, 2015