Geodesic
.Cloning operations and graph diameter
Diskretnaya Matematika, Tome 34 (2022) no. 2, pp. 26-31.

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

The influence of the subgraph cloning operation on the graph diameter is studied. The corresponding potential increase in the diameter is estimated. Conditions under which the subgraph cloning operation causes no change in the graph diameter are formulated. An example of using the cloning operation to construct a family of fat trees is presented. The diameter of such graphs and the complexity of their design are estimated.
Keywords: graph, eccentricity, diameter, cloning operation, support vertex. 
@article{DM_2022_34_2_a2,
     author = {M. A. Iordanskii},
     title = {.Cloning operations and graph diameter},
     journal = {Diskretnaya Matematika},
     pages = {26--31},
     publisher = {mathdoc},
     volume = {34},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2022_34_2_a2/}
}
TY  - JOUR
AU  - M. A. Iordanskii
TI  - .Cloning operations and graph diameter
JO  - Diskretnaya Matematika
PY  - 2022
SP  - 26
EP  - 31
VL  - 34
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2022_34_2_a2/
LA  - ru
ID  - DM_2022_34_2_a2
ER  - 
%0 Journal Article
%A M. A. Iordanskii
%T .Cloning operations and graph diameter
%J Diskretnaya Matematika
%D 2022
%P 26-31
%V 34
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2022_34_2_a2/
%G ru
%F DM_2022_34_2_a2
M. A. Iordanskii. .Cloning operations and graph diameter. Diskretnaya Matematika, Tome 34 (2022) no. 2, pp. 26-31. http://geodesic.mathdoc.fr/item/DM_2022_34_2_a2/

[1] M. A. Iordanskii, “Konstruktivnye opisaniya grafov”, Diskretnyi analiz i issledovanie operatsii, 3:4 (1996), 35–63 | MR | Zbl

[2] Iordanskii M. A., Konstruktivnaya teoriya grafov i ee prilozheniya, Kirillitsa, N. Novgorod, (2016), 172 pp.

[3] Iordanski M. A., Constructive graph theory: generation methods, structure and dynamic characterization of closed classes of graphs - a survey, 2020, arXiv: 2011.10984

[4] Iordanskii M. A., “Klonirovanie grafov”, Problemy teoreticheskoi kibernetiki, Mater. XVIII mezhdunar. konf. (Penza), MAKS Press, Moskva, 2017, 108–110

[5] Iordanskii M. A., “O slozhnosti sinteza grafov operatsiyami klonirovaniya”, Diskretnaya matematika i ee prilozheniya, Mater. XIII mezhdunar. sem. (Moskva), izd-vo mekh.-matem. f-ta MGU, Moskva, 2019, 220–223

[6] Rappoport A. M., “Metricheskie kharakteristiki grafov setei kommunikatsii”, Trudy In-ta sistemn. analiza Rossiiskoi akademii nauk, 14 (2005), 141–147

[7] Melentiev V. A., “On scalability of computing systems with compact topology”, Theor. Appl. Sci., 11:43 (2016), 164–169 | DOI

[8] Leiserson C. E., “Fat-trees: universal networks for hardware-efficient supercomputing”, IEEE Trans. Comput., C-34 (1985), 892–901 | DOI

[9] Berzh K., Teoriya grafov i ee primeneniya, M.: IL, 1962, 319 pp.