About a counterexample on contractible transformations of graphs

Abstract

In [A. V. Ivashchenko, Contractible transformations do not change the homology groups of graphs, Discrete Mathematics 126 (1) (1994) p 159,170], Ivashchenko started with the study of contractible graphs, he began with this because they have application to molecular spaces. But in a second paper [A. V. Ivashchenko, Some properties of contractible transformations on graphs, Discrete Mathematics 133 (1) (1994) p 139,145], he made several mistakes. We show in this paper that the results in that second paper are false or the proofs are wrong.