EN|RU Volume 18, No 1, 2011, P. 77-84 UDC 519.87 E. A. Monakhova On an extremal family of circulant networks Abstract: We consider the problem of maximization of the number of nodes of circulant networks for a given degree and diameter. The estimate of the diameter of graphs of the best known extremal family of circulant networks is improved that together with results given earlier for multiplicative circulant graphs allowed to improve the lower estimates of attainable number of nodes of circulant networks for any dimension $k\ge4$. Bibliogr. 12. Keywords: circulant network, diameter, maximal order of a graph. Monakhova Emilia Anatol’evna 1 1. Institute of Computational Technologies, 6 Acad. Lavrent’ev ave., 630090 Novosibirsk, Russia e-mail: emilia@rav.sscc.ru © Sobolev Institute of Mathematics, 2015