  Recently, in the paper \cite{CJKM1} we suggested the two conjectures about
the diameter of io-decomposable Riordan graphs of the Bell type. In this paper,
we give a counterexample for the first conjecture. Then we prove that the first
conjecture is true for the graphs of some particular size and propose a new
conjecture. Finally, we show that the second conjecture is true for some
special io-decomposable Riordan graphs.
