Literature review indicates that some researchers tended to classify the vertex-multiplication graphs corresponding to third-order connected astatic graphs into three categories

and made the hypothesis that the category-Ⅲ graph does not include the vertex-multiplication graph corresponding to the connected astatic graph with its diameter being at lest 3.In this paper

the author has proved that the hypothesis hereinabove goes to trees by employing vertex grading approach: the minimum number of oriented diameter of tree vertex-multiplication graphs has increased by 1 compared with that of the original tree.