Yes, for for every vertex gets an entry in the list created, but you list has some small by using an int pointer, but using a cast to insert an entry.
Important tip: use for the class member V a long and better name like "index" or vertex to seperate it clearer from input vars. Vars are normally in lower case.
The code gets clearer and more fun to read:
this->vertex = v;
adjList = new std::list<int>[v];