Mother Vertex in Graph

 It is a vertex v such that all other vertices in G can be reached by a path from v.

Solution:

step1: first we need to do DFS on each vertex and get the value of vertex when all value of visited array true.

step2: need to DFS on selected value if all the vertex visited it means the value is mother vertex.

public class MotherVertex {

    public MotherVertex() {

    }

    void addEdge(ArrayList<ArrayList<Integer>> adj, int v, int u){
         adj.get(v).add(u);
     }

    public static void main(String[] args) {
        ArrayList<ArrayList<Integer>> adj = new ArrayList<>();
        for(int i=0;i<7;i++){
            adj.add(new ArrayList<>());
        }
        MotherVertex g = new MotherVertex();
        g.addEdge(adj,0, 1);
        g.addEdge(adj,0, 2);
        g.addEdge(adj,1, 3);
        g.addEdge(adj,4, 1);
        g.addEdge(adj,6, 4);
        g.addEdge(adj,6, 0);
        g.addEdge(adj,5, 2);
        g.addEdge(adj,5, 6);

        g.motherVertex(adj,7);
    }

    void motherVertex(ArrayList<ArrayList<Integer>> adj,int V){

//dfs on all vertex
        boolean[] visited = new boolean[V];
        for(int i=0;i<visited.length;i++){
            visited[i]=false;
        }
        int val= -1;
        for(int i=0;i<V;i++){
            if(!visited[i]) {
                DFS(i, adj, visited);
                val = i;
            }
        }

//selected value when visited array value get true
        System.out.println(val);

//dfs on selected value
        visited = new boolean[V];
        DFS(val,adj,visited);
        for (int i=0;i<7;i++){
            if(!visited[i]){
                System.out.println("not found mother vertex");
                return;
            }
        }

//if all value of visited array is true then its mother vertex
        System.out.println("mother vertex"+val);
    }

    void DFS(int v,ArrayList<ArrayList<Integer>> adj,boolean[] visited){



        visited[v]=true;


          //  System.out.println(v);
            ArrayList<Integer> list = adj.get(v);
            Iterator<Integer> iterator = list.iterator();
            while (iterator.hasNext()){
                Integer i = iterator.next();
                if(!visited[i]){
                   DFS(i,adj,visited);
                }
        }
    }
}

output: 

5

mother vertex 5