Overall a good design. However there are few points which you should pay attention to.
Access Modifiers You code has some properties as public and also public getter. This makes no sense. You should choose the access modifiers carefully. Anybody can access the child (NodeArray) and set to null if this code is used as an API by some user.
public Node[] child;
public Node[] getChild() { return child; }
public class Graph {
public int count; // num of vertices
Static Functions Your DFS and BFS functions are not static. I can think of no reason to do that when you have create function as static. Better make it consistent.