Geodesic
A new attainable lower bound on the number of nodes in quadruple circulant networks
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 1, pp. 37-44.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DA_2013_20_1_a3,
     author = {E. A. Monakhova},
     title = {A new attainable lower bound on the number of nodes in quadruple circulant networks},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {37--44},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2013_20_1_a3/}
}
TY  - JOUR
AU  - E. A. Monakhova
TI  - A new attainable lower bound on the number of nodes in quadruple circulant networks
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2013
SP  - 37
EP  - 44
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2013_20_1_a3/
LA  - ru
ID  - DA_2013_20_1_a3
ER  - 
%0 Journal Article
%A E. A. Monakhova
%T A new attainable lower bound on the number of nodes in quadruple circulant networks
%J Diskretnyj analiz i issledovanie operacij
%D 2013
%P 37-44
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2013_20_1_a3/
%G ru
%F DA_2013_20_1_a3
E. A. Monakhova. A new attainable lower bound on the number of nodes in quadruple circulant networks. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 1, pp. 37-44. http://geodesic.mathdoc.fr/item/DA_2013_20_1_a3/

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

[2] Monakhova E. A., “Strukturnye i kommunikativnye svoistva tsirkulyantnykh setei”, Prikl. diskret. matematika, 13:3 (2011), 92–115

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

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

[5] Dougherty R., Faber V., “The degree-diameter problem for several varieties of Cayley graphs. 1: The abelian case”, SIAM J. Discrete Math., 17:3 (2004), 478–519 | DOI | MR | Zbl

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

[7] Macbeth H., Siagiova J., Siran J., “Cayley graphs of given degree and diameter for cyclic, abelian, and metacyclic groups”, Discrete Math., 312:1 (2012), 94–99 | DOI | MR | Zbl

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

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