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. 
@article{PDMA_2014_7_a56,
     author = {D. U. Osipov},
     title = {On a~counterexample for {a~T-irreducible} extensions of star-like trees},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {132--135},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2014_7_a56/}
}
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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/