Geodesic
On an extremal family of circulant networks
Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 1, pp. 77-84.

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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. 
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E. A. Monakhova. On an extremal family of circulant networks. Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 1, pp. 77-84. http://geodesic.mathdoc.fr/item/DA_2011_18_1_a7/

[1] Monakhov O. G., Monakhova E. A., Parallelnye sistemy s raspredelennoi pamyatyu: struktury i organizatsiya vzaimodeistvii, Izd-vo SO RAN, Novosibirsk, 2000, 242 pp.

[2] Monakhova E. A., “Optimizatsiya tsirkulyantnykh setei svyazi razmernosti chetyre”, Diskret. analiz i issled. operatsii, 15:3 (2008), 58–64 | MR

[3] Monakhova E. A., “Multiplikativnye tsirkulyantnye seti”, Diskret. analiz i issled. operatsii, 17:5 (2010), 56–66

[4] Bermond J.-C., Comellas F., Hsu D. F., “Distributed loop computer networks: a survey”, J. Parallel Distributed Comput., 24 (1995), 2–10 | DOI

[5] Chen S., Jia X.-D., “Undirected loop networks”, Networks, 23 (1993), 257–260 | DOI | MR | Zbl

[6] Hwang F. K., “A survey on multi-loop networks”, Theoret. Comput. Sci., 299 (2003), 107–121 | DOI | MR | Zbl

[7] Monakhov O. G., Monakhova E. A., “Computer discovery of analytical descriptions of families of circulant networks”, Proc. 6th Intern. Conf. Soft Computing and Measurements, SCM' 2003 (St.-Petersburg, Russia, 2003), v. 1, LETI, St. Petersburg, 2003, 345–348

[8] Monakhova E., “Optimal triple loop networks with given transmission delay: topological design and routing”, Proc. Intern. Network Optimization Conf., INOC' 2003 (Evry/Paris, France, 2003), INT, Paris, 2003, 410–415

[9] Muga F. P., “Undirected circulant graphs”, Proc. Intern. Symp. Parallel Architectures, Algorithms, and Networks, IEEE Press, Los Alamitos, 1994, 113–118

[10] Parhami B., “A class of odd-radix chordal ring networks”, The CS'J J. Comput. Sci. Engineering, 4:2–4 (2006), 1–9

[11] Stojmenovic I., “Multiplicative circulant networks. Topological properties and communication algorithms”, Discrete Appl. Math., 77 (1997), 281–305 | DOI | MR | Zbl

[12] Wong C. K., Don Coppersmith, “A combinatorial problem related to multimodule memory organizations”, J. Assoc. Comput. Mach., 21 (1974), 392–402 | MR | Zbl