Geodesic
On a~counterexample for a~T-irreducible extensions of star-like trees
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 132-135.

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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. 
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     author = {D. U. Osipov},
     title = {On a~counterexample for {a~T-irreducible} extensions of star-like trees},
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D. U. Osipov. On a~counterexample for a~T-irreducible extensions of star-like trees. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 132-135. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a56/

[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 eë 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