Can anyone explain the how the size of an Euler Tour Tree(ETT) array is 2*no.of vertices.

please read the ETT of type 3 in this LCA, in ETT of type 2, it is quite clear that we need double the space of total vertices to store the ETT as all vertices are added exactly twice(one for entry and one for exit).

In ETT of type 3, it is mentioned that a vertice is added each time it is visited, now my conclusion is that, a node will be added exactly (1 + no.of children it has), now i am not able to deduce how only 2 * total vertices are needed, as claimed in this article.