Geodesic
Upper bound for the number of additional edges in minimal $1$-edge extensions of starlike trees
Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 91-99.

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

Minimal edge extension of graphs can be regarded as a model of optimal edge fault tolerant implementation of a system. This paper is about an upper bound for the number of additional edges in minimal $1$-edge extensions for graphs of a special class – starlike trees. Two schemes for constructing $1$-edge extensions for any kind starlike trees and an algorithm based on these schemes are proposed.
Keywords: graphs, minimal extensions of graphs, fault tolerance, starlike trees. 
@article{PDM_2015_4_a8,
     author = {D. D. Komarov},
     title = {Upper bound for the number of additional edges in minimal $1$-edge extensions of starlike trees},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {91--99},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_4_a8/}
}
TY  - JOUR
AU  - D. D. Komarov
TI  - Upper bound for the number of additional edges in minimal $1$-edge extensions of starlike trees
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2015
SP  - 91
EP  - 99
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2015_4_a8/
LA  - ru
ID  - PDM_2015_4_a8
ER  - 
%0 Journal Article
%A D. D. Komarov
%T Upper bound for the number of additional edges in minimal $1$-edge extensions of starlike trees
%J Prikladnaâ diskretnaâ matematika
%D 2015
%P 91-99
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2015_4_a8/
%G ru
%F PDM_2015_4_a8
D. D. Komarov. Upper bound for the number of additional edges in minimal $1$-edge extensions of starlike trees. Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 91-99. http://geodesic.mathdoc.fr/item/PDM_2015_4_a8/

[1] Abrosimov M. B., “On the complexity of some problems related to graph extensions”, Mat. Zametki, 88:5 (2010), 643–650 (in Russian) | DOI | MR | Zbl

[2] Abrosimov M. B., “On lower bound of edge number of minimal edge 1-extension of starlike tree”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 11:3(2) (2011), 111–117 (in Russian)

[3] Harary F., Hayes J. P., “Edge fault tolerance in graphs”, Networks, 23 (1993), 135–142 | DOI | MR | Zbl

[4] Abrosimov M. B., Graph Model of Fault Tolerance, SSU Publ., Saratov, 2012, 192 pp. (in Russian)

[5] Abrosimov M. B., Komarov D. D., Minimal Edge 1-Extension of Starlike Trees with a Small Number of Vertices, Dep. VINITI 18.10.2010, No. 589-V, Saratov, 2010, 27 pp. (in Russian)