Geodesic
On the problem of circulant networks with the maximal number of nodes for any diameter
Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 81-85

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

For undirected circulant networks, the problem of the maximal reachable number of nodes under given dimension and diameter of a graph is considered. In 1994, F. P. Muga proved the theorem that this number is odd for any dimension and any diameter of a circulant graph. Later, R. R. Lewis has presented a counterexample of four-dimensional circulant. In the present paper, a mistake in the proof of this theorem is pointed. Based on the new results, the early presented table of the maximal reachable orders of four-dimensional circulants is corrected.
Keywords: undirected circulant graphs, diameter, maximum order of a graph. 
@article{PDM_2014_3_a6,
     author = {E. A. Monakhova and O. G. Monakhov},
     title = {On the problem of circulant networks with the maximal number of nodes for any diameter},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {81--85},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_3_a6/}
}
TY  - JOUR
AU  - E. A. Monakhova
AU  - O. G. Monakhov
TI  - On the problem of circulant networks with the maximal number of nodes for any diameter
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2014
SP  - 81
EP  - 85
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2014_3_a6/
LA  - ru
ID  - PDM_2014_3_a6
ER  - 
%0 Journal Article
%A E. A. Monakhova
%A O. G. Monakhov
%T On the problem of circulant networks with the maximal number of nodes for any diameter
%J Prikladnaâ diskretnaâ matematika
%D 2014
%P 81-85
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2014_3_a6/
%G ru
%F PDM_2014_3_a6
E. A. Monakhova; O. G. Monakhov. On the problem of circulant networks with the maximal number of nodes for any diameter. Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 81-85. http://geodesic.mathdoc.fr/item/PDM_2014_3_a6/