Geodesic
On a~counterexample for a~T-irreducible extensions of starlike trees
Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 98-102.

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

T-irreducible extension of a graph $G$ is an extension of the graph $G$ which is obtained by removing maximal set of edges from the trivial extension of $G$. Here, counterexample is shown for the method by F. Harary and M. Khurum for constructing one of T-irreducible extensions for star-like trees. Besides, all nonisomorphic T-irreducible extensions are constructed for star-like trees with rays of equal length.
Keywords: graph, T-irreducible extension, star-like trees, star-like trees with rays of equal length. 
@article{PDM_2014_3_a8,
     author = {D. U. Osipov},
     title = {On a~counterexample for {a~T-irreducible} extensions of starlike trees},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {98--102},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_3_a8/}
}
TY  - JOUR
AU  - D. U. Osipov
TI  - On a~counterexample for a~T-irreducible extensions of starlike trees
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2014
SP  - 98
EP  - 102
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2014_3_a8/
LA  - ru
ID  - PDM_2014_3_a8
ER  - 
%0 Journal Article
%A D. U. Osipov
%T On a~counterexample for a~T-irreducible extensions of starlike trees
%J Prikladnaâ diskretnaâ matematika
%D 2014
%P 98-102
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2014_3_a8/
%G ru
%F PDM_2014_3_a8
D. U. Osipov. On a~counterexample for a~T-irreducible extensions of starlike trees. Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 98-102. http://geodesic.mathdoc.fr/item/PDM_2014_3_a8/

[1] Bogomolov A. M., Salii V. N., Algebraicheskie osnovy teorii diskretnykh sistem, Nauka, M., 2009 | MR

[2] Abrosimov M. B., “Minimalnye rasshireniya ob'edineniya nekotorykh grafov”, Teoreticheskie problemy informatiki i ee prilozhenii, 2001, no. 4, 3–11

[3] Salii V. N., “Dokazatelstva s nulevym razglasheniem v zadachakh o rasshireniyakh grafov”, Vestnik Tomskogo gosudarstvennogo universiteta. Prilozhenie, 2003, no. 6, 63–65

[4] Harary F., Khurum M., “One node fault tolerance for caterpillars and starlike trees”, Internet J. Comput. Math., 6 (1995), 135–143 | DOI

[5] Abrosimov M. B., Komarov D. D., “Ob odnom kontrprimere dlya minimalnykh vershinnykh 1-rasshirenii sverkhstroinykh derevev”, Prikladnaya diskretnaya matematika. Prilozhenie, 2012, no. 5, 83–84

[6] Osipov D. Yu., “O T-neprivodimykh rasshireniyakh sverkhstroinykh derevev”, Prikladnaya diskretnaya matematika. Prilozhenie, 2013, no. 6, 85–86 | MR