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.