Solution: Implement Breadth First Search

class CheckBFS {
    public static String bfs(Graph g){
        
        String result = "";
        //Checking if the graph has no vertices
        if (g.vertices < 1){
            return result;
        }
        //Boolean Array to hold the history of visited nodes (by default-false)
        boolean[] visited = new boolean[g.vertices];
    
        for(int i=0;i<g.vertices;i++) 
        { 
            //Checking whether the node is visited or not 
            if(!visited[i]) 
            { 
                result = result + bfsVisit(g, i, visited); 
            } 
        }
        return result;
    }
    public static String bfsVisit(Graph g, int source, boolean[] visited) {
        
        String result = "";
        //Create Queue for Breadth First Traversal and enqueue source in it
        Queue<Integer> queue = new Queue<>(g.vertices);
        queue.enqueue(source);
        visited[source] = true;
        //Traverse while queue is not empty
        while (!queue.isEmpty()) {
            //Dequeue a vertex/node from queue and add it to result
            int current_node = queue.dequeue();
            result += String.valueOf(current_node);
            //Get adjacent vertices to the current_node from the array,
            //and if they are not already visited then enqueue them in the Queue
            DoublyLinkedList<Integer>.Node temp = null;
            if(g.adjacencyList[current_node] != null)
                temp = g.adjacencyList[current_node].headNode;
            while (temp != null) {
                if (!visited[temp.data]) {
                    queue.enqueue(temp.data);
                    visited[temp.data] = true; //Visit the current Node
                }
                temp = temp.nextNode;
            }
        }//end of while
        return result;
    }
    public static void main(String args[]) {
        Graph g = new Graph(5);
        g.addEdge(0,1);
        g.addEdge(0,2);
        g.addEdge(1,3);
        g.addEdge(1,4);
        System.out.println("Graph1:");
        g.printGraph();
        System.out.println("BFS traversal of Graph1 : " + bfs(g));
        System.out.println();
        Graph g2 = new Graph(5);
        g2.addEdge(0,1);
        g2.addEdge(0,4);
        g2.addEdge(1,2);
        g2.addEdge(3,4);
        System.out.println("Graph2:");
        g2.printGraph();
        System.out.println("BFS traversal of Graph2 : " + bfs(g2));
  }
}