Geodesic
Multiplicative circulant networks
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 5, pp. 56-66.

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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 $k\ge4$. The infinite families of circulant networks attaining the found bounds are constructed. Bibliogr. 13.
Keywords: circulant network, diameter, maximal order of a graph. 
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E. A. Monakhova. Multiplicative circulant networks. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 5, pp. 56-66. http://geodesic.mathdoc.fr/item/DA_2010_17_5_a5/

[1] Martines K., Stafford E., Baivide R., Gabidulin E. M., “Predstavlenie geksagonalnykh sozvezdii s pomoschyu grafov Eizenshteina–Yakobi”, Probl. peredachi inf., 44:1 (2008), 3–14 | MR | Zbl

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

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

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

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

[6] Garcia C., Sole P., “Diameter lower bounds for Waring graphs and multiloop networks”, Discrete Math., 111 (1993), 257–261 | DOI | MR | Zbl

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

[8] Liaw S.-C., Chang G. J., Cao F., Hsu D. F., “Fault-tolerant routing in circulant networks and cycle prefix networks”, Ann. Combin., 2 (1998), 165–172 | DOI | MR | Zbl

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

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

[11] Parhami B., “Chordal rings based on symmetric odd-radix number systems”, Proc. Int. Conf. Communications in Computing (Las Vegas, NV, June 27–30, 2005), IEEE Press, Los Alamitos, 2005, 196–199

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

[13] Wong C. K., Coppersmith D., “A combinatorial problem related to multimodule memory organizations”, J. ACM, 21:3 (1974), 392–402 | DOI | MR | Zbl