On a counterexample for a T-irreducible extensions of starlike trees
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.