Detect Cycle in an Undirected Graph

Detect Cycle in an Undirected Graph

Here given code implementation process.

//C Program 
//Detect Cycle in a Undirected Graph
#include<stdio.h>
#include<stdlib.h>

struct AjlistNode
{
  //Vertices id
  int vId;
  struct AjlistNode*next;
};

struct Graph
{
  //node key value
  int data;
  struct AjlistNode*next;
};
void setData(struct Graph *);
int size; //number of nodes

//set node key value
void setData(struct Graph*node)
{
  if(node!=NULL && size>0)
  {
    int index=0;
    for(index;index<size;index++)
    {
            //set vertic node data
      node[index].data=index;//set node key
      //Initial no AjlistNode
      //set NULL Value
      node[index].next=NULL;
    }
  }else
  {
    printf("Vertic Node is Empty");
  }
}

void connect_edge(struct Graph*node, int V ,int E)
{

    // create Adjacency node
  struct AjlistNode *newEdge=(struct AjlistNode*)malloc(
    sizeof(struct AjlistNode)
    );
  if(newEdge!=NULL)
  {

    newEdge->next=NULL;
    newEdge->vId=E;

    struct AjlistNode *temp=node[V].next;

    if(temp==NULL)
    {
      node[V].next=newEdge;
    }else
    {
            //Add node at last
      while(temp->next!=NULL)
      {
        temp=temp->next;
      }      
      temp->next=newEdge;          
    }
  }else
  {
    printf("\n Memory overflow");

  }
}
//Add Edge from Two given Nodes
void addEdge(struct Graph*node, int V ,int E)
{
    //add edge form V to E
    //V and E is Node location
  if(V<size && E <size)
  {

    connect_edge(node,V,E);
    connect_edge(node,E,V);

  }else
  {
        //not valid Vertices
    printf("Invalid Node Vertices %d  %d", V,E);
  }
}
//Display Adjacency list of vertex
void printGraph(struct Graph*node)
{
  if(node!=NULL)
  {
    struct AjlistNode *temp=NULL;
    for(int index=0;index<size;index++)
    {
      printf("\n Adjacency list of vertex %d  :",index);
      temp=node[index].next;
      while(temp!=NULL)
      {
        //temp->vId is graph node vertices
        //in this case temp->vId is same as 
        //node[temp->vId].data

        printf("  %d",node[temp->vId].data);
        temp=temp->next;
      }
    }
  }else
  {
    printf("Empty Graph");
  }
}

void detect_cycle(int point,int *visit,struct Graph*node)
{
  if(visit[point]>=1)
  {

    visit[point]=visit[point]+1;

    return;
  }
  visit[point]=1;
  struct AjlistNode *temp=node[point].next;
  int counter=0;
  while(temp!=NULL)
  {
    counter++;
    detect_cycle(temp->vId,visit,node); 
    temp=temp->next;
  }
  
  if(counter>0)
  {
    visit[point]=visit[point]-counter;
    if(visit[point]<0)
    {
      visit[point]=-visit[point];
    }
  }


}
void check_cycle(struct Graph*node)
{

  if(node==NULL)
  {
    printf("Empty Graph\n");
    return;
  }
  printGraph(node);
  int *visit=(int*)calloc(size,sizeof(int));
  int test=0,status=0;

  detect_cycle(test,visit,node);

  printf("\n result : ");
  for(int index=0;index<size;index++)
  {

    if(index==0&&visit[index]==1)
    {
      //This are start vertex
      continue;
    }
    if(visit[index]>0)
    {
      status=1;
      break;
    }
  }
  if(status==1)
  {
    printf("Yes\n");
  }else
  {
    printf("No\n"); 
  }
}
int main()
{

  size=6;
  struct Graph*node=node=(struct Graph*)malloc(
    sizeof(struct Graph)*size
    );

  if(node==NULL)
  {
    printf("\n Memory overflow");
  }else
  {
    //First set node keys
    setData(node); 
    //Connected two node with Edges

    addEdge(node,0,1);
    addEdge(node,0,2);
    addEdge(node,1,3);
    addEdge(node,1,4);

    addEdge(node,2,5);

    check_cycle(node);

    addEdge(node,5,4);

    //Case two
    check_cycle(node);
  }  

  return 0;
}

Output

 Adjacency list of vertex 0  :  1  2
 Adjacency list of vertex 1  :  0  3  4
 Adjacency list of vertex 2  :  0  5
 Adjacency list of vertex 3  :  1
 Adjacency list of vertex 4  :  1
 Adjacency list of vertex 5  :  2
 result : No

 Adjacency list of vertex 0  :  1  2
 Adjacency list of vertex 1  :  0  3  4
 Adjacency list of vertex 2  :  0  5
 Adjacency list of vertex 3  :  1
 Adjacency list of vertex 4  :  1  5
 Adjacency list of vertex 5  :  2  4
 result : Yes
//C++ program
//Detect Cycle in a Undirected Graph
#include<iostream>
using namespace std;

struct AjlistNode
{
    int vId;//Vertices id
    struct AjlistNode*next;
};

struct Vertices
{
    int data; //node key value
    struct AjlistNode*next;
};

class Graph
{
	Vertices *node;
    int size;//number of 
public:
	Graph(int);
	void setData();
	void addEdge(int,int);
	void printGraph();
	void check_cycle();
	void detect_cycle(int ,int []);
	void connect(int ,int );
};
Graph::Graph(int size)
{
	this->size = size;
    //set number of nodes
	node = new Vertices[size];
}
//set node key value
void Graph:: setData()
{
	if(node!=NULL)
	{
		int index=0;

		for(index;index<size;index++)
		{
			//set vertic node data
			node[index].data=index;//set node key
			//Initial no AjlistNode
			//set NULL Value
			node[index].next=NULL;
		}
	}
	else
	{
		cout<<"Vertic Node is Empty"<<endl;
	}
}
//Add Edge from Two given Nodes
void Graph ::connect(int V ,int E)
{
    //add edge form V to E
    //V and E is Node location
    //first create Adjacency node
	AjlistNode *newEdge=new AjlistNode;

	if(newEdge!=NULL)
	{

		newEdge->next=NULL;
		newEdge->vId=E;

		AjlistNode *temp=node[V].next;

		if(temp==NULL)
		{
			node[V].next=newEdge;
		}else
		{
            //Add node at last
			while(temp->next!=NULL)
			{
				temp=temp->next;
			}      
			temp->next=newEdge;          
		}
	}

}


void Graph ::addEdge(int V ,int E)
{
    //add edge form V to E
    //V and E is Node location
	if(V<size && E <size)
	{
		connect(V,E);
		if(V==E)
        {   //self loop
        	return;
        }
        connect(E,V);

    }else
    {
        //not valid Vertices
    	cout<<"Invalid Node Vertices "<< V<<" "<<E;
    }
}

//Display Adjacency list of vertex
void Graph::printGraph()
{
	if(node!=NULL)
	{
		AjlistNode *temp=NULL;
		for(int index=0; index < size; index++)
		{
			cout<<"\n Adjacency list of vertex "<<index<<" :";
			temp=node[index].next;
			while(temp!=NULL)
			{
                //temp->vId is graph node vertices
                //in this case temp->vId is same as 
                //node[temp->vId].data

				cout<<" "<<node[temp->vId].data;
				temp=temp->next;
			}
		}
	}else
	{
		cout<<"Empty Graph"<<endl;
	}
}
//Detect cycle using DFS
void Graph:: detect_cycle(int point,int visit[])
{

	if(visit[point]>=1)
	{

		visit[point]=visit[point]+1;

		return;
	}
	visit[point]=1;
	struct AjlistNode *temp=node[point].next;
	int counter=0;
	while(temp!=NULL)
	{
		counter++;
		detect_cycle(temp->vId,visit); 
		temp=temp->next;
	}

	if(counter>0)
	{
		visit[point]=visit[point]-counter;
		if(visit[point]<0)
		{
			visit[point]=-visit[point];
		}
	}
}
//method which are manage finding and detecting cycle operation
void Graph:: check_cycle()
{

	if(node==NULL)
	{
		cout<<("Empty Graph\n");
		return;
	}
	printGraph();
	
	int test=0,status=0;

	int *visit= new int[size];
    for (int i = 0; i < size; ++i)
    {
    	visit[i]=0;
    }
	detect_cycle(test,visit);
    
	cout<<"\n result : ";
	for(int index=0;index<size;index++)
	{

		if(index==0&&visit[index]==1)
		{
	      //This are start vertex
			continue;
		}
		if(visit[index]>0)
		{
			status=1;
			break;
		}
	}
	if(status==1)
	{
		cout<<" Yes\n";
	}else
	{
		cout<<" No \n";
	}
}

int main()
{
    //Create Object
	Graph g(6);
    //First set node keys
	g.setData();

	g.addEdge(0,1);
	g.addEdge(0,2);
	g.addEdge(1,3);
	g.addEdge(1,4);

	g.addEdge(2,5);

	g.check_cycle();

	g.addEdge(5,4);

        //Case two
	g.check_cycle();

	return 0;
}

Output

 Adjacency list of vertex 0 : 1 2
 Adjacency list of vertex 1 : 0 3 4
 Adjacency list of vertex 2 : 0 5
 Adjacency list of vertex 3 : 1
 Adjacency list of vertex 4 : 1
 Adjacency list of vertex 5 : 2
 result :  No 

 Adjacency list of vertex 0 : 1 2
 Adjacency list of vertex 1 : 0 3 4
 Adjacency list of vertex 2 : 0 5
 Adjacency list of vertex 3 : 1
 Adjacency list of vertex 4 : 1 5
 Adjacency list of vertex 5 : 2 4
 result :  Yes
//Java program
//Detect Cycle in a Undirected Graph
public class MyGraph
{

    static class AjlistNode
    {
        int id;//Vertices node key
        AjlistNode next;
    }
    static class Vertices
    {
        int data;
        AjlistNode next;
    }

    //number of Vertices
    static int size;
    Vertices node[];

    MyGraph(int size)
    {
        //set value
        this.size = size;
        node = new Vertices[size];
        
    }

    //set initial node value
    public void setData()
    {
        if(node == null)
        {
            System.out.println("\nEmpty Graph");
        }else
        {
            for(int index = 0; index < size; index++)
            {
                // avoid java.lang.nullPointerException
                node[index]=new Vertices(); 
                node[index].data=index;//set your data
                node[index].next=null;
            }
        }
    }
    //connect two nodes
    public void connect(int start,int end)
    {
        AjlistNode newEdge=new AjlistNode();
            newEdge.id=end;//end node
            newEdge.next=null;
            if(node[start].next==null)
            {
                node[start].next=newEdge;
            }else
            {
                AjlistNode temp=node[start].next;

                while(temp.next!=null)
                {
                    temp=temp.next;
                }
                temp.next=newEdge;
            }
    }
    //Add edge at the end
    public void addEdge(int start,int end)
    {
        if(start < size && end < size && node != null)
        {
           connect(start,end);
           if(start==end)
           {
            //self loop
            return;
           }
           connect(end,start);
        }else{
            System.out.println("\nEmpty Graph");
        }
    }

    public void printGraph()
    {

        if(size>0 && node!=null)
        {
            for(int index=0;index<size;index++)
            {
                System.out.print("\nAdjacency list of vertex "+index+" :");
                
                AjlistNode temp=node[index].next;

                while(temp!=null)
                {
                    System.out.print(" "+node[temp.id].data);

                    temp=temp.next;
                }
            }
        }
    }
    //Detect cycle using DFS
    public void detectCycle(int point,int visit[])
    {

        if(visit[point] >= 1)
        {

            visit[point]=visit[point]+1;
            return;
        }
        visit[point]=1;

        AjlistNode  temp=node[point].next;
        int counter=0;
        while(temp!=null)
        {
            counter++;
            detectCycle(temp.id,visit); 
            temp=temp.next;
        }

        if(counter>0)
        {
            visit[point] = visit[point]-counter;

            if(visit[point]<0)
            {
                visit[point]=-visit[point];
            }
        }
    }
    //method which are manage finding and detecting cycle operation
    public void checkCycle()
    {  

        if(node==null)
        {
            System.out.println("Empty Graph");
            return;
        }

        printGraph();

        //This are storing the information about visiting node status
        int []visit=new int[size];
        
        for(int index=0;index < size; index++)
        {
           visit[0]=0;
        }
        detectCycle(0,visit); 

        int test=0,status=0;

        System.out.print("\nresult : ");

        for(int index=0;index < size; index++)
        {

            if(index==0 && visit[index]==1)
            {
                //This are start vertex
                continue;
            }
            if(visit[index]>0)
            {
                status=1;
                break;
            }
        }
        if(status==1)
        {
            System.out.println("Yes");
        }else
        {
            System.out.println("No ");
        }
    }

    public static void main(String[] args) 
    {
        int totalNode=6;

        MyGraph g=new MyGraph(totalNode);
        g.setData();
        //Connected two node with Edges

        g.addEdge(0,1);
        g.addEdge(0,2);
        g.addEdge(1,3);
        g.addEdge(1,4);

        g.addEdge(2,5);

        g.checkCycle();

        g.addEdge(5,4);

        //Case two
        g.checkCycle();

    }
}

Output

Adjacency list of vertex 0 : 1 2
Adjacency list of vertex 1 : 0 3 4
Adjacency list of vertex 2 : 0 5
Adjacency list of vertex 3 : 1
Adjacency list of vertex 4 : 1
Adjacency list of vertex 5 : 2
result : No 

Adjacency list of vertex 0 : 1 2
Adjacency list of vertex 1 : 0 3 4
Adjacency list of vertex 2 : 0 5
Adjacency list of vertex 3 : 1
Adjacency list of vertex 4 : 1 5
Adjacency list of vertex 5 : 2 4
result : Yes
#Python program
#Detect Cycle in a Undirected Graph
class AjLinkeNode:
  def __init__(self,data):
    self.id=data
    self.next=None

class Vertices:
  def __init__(self,data):
    self.data=data
    self.next=None

class Graph:
  """Constructor for Graph"""
  def __init__(self, size):
    self.size=size
    self.node=[]
    

  def setData(self):
    if(self.size>0 and self.node!=None):
      index=0
      while(index<self.size):
        self.node.append(Vertices(index))
        index+=1
  #connect two node with  edge
  def connect(self,start,end):
    new_edge=AjLinkeNode(end)
    if(self.node[start].next==None):
      self.node[start].next=new_edge
    else:
      temp=self.node[start].next
      while(temp.next!=None):
        temp=temp.next
      temp.next=new_edge      
  #add edge
  def addEdge(self,start,end):

    #start,end is two nodes
    if(self.size>start and self.size>start):
      
      self.connect(start,end)
      if(start == end):
        return
      self.connect(end,start)  

    else:
      print("Invalid nodes")


  def printGraph(self):

    if(self.size>0 and self.node!=None):

      index=0

      while(index<self.size):

        print("\nAdjacency list of vertex  {0} :".format(index),end=" ")
        
        temp=self.node[index].next
        
        while temp!=None:

          print("  {0}".format(temp.id),end=" ")

          temp=temp.next

        index+=1

  #Detect cycle using DFS
  def detectCycle(self, point, visit):


    if(visit[point] >= 1):
      visit[point]=visit[point]+1
      return
    
    visit[point]=1

    temp=self.node[point].next
    counter=0
    while(temp!=None):
      counter+=1
      self.detectCycle(temp.id,visit) 
      temp=temp.next
    

    if(counter>0):
      visit[point] = visit[point]-counter

      if(visit[point]<0):
        visit[point]=-visit[point]
        
    

    
    #method which are manage finding and detecting cycle operation
  def checkCycle(self):

    if(self.node==None):
      print("Empty Graph")
      return
    

    self.printGraph()

    #This are storing the information about visiting node status
    visit=[0]*self.size

    self.detectCycle(0,visit); 
    status=0
    index=0
    print("\nresult : ",end="")
    while(index < self.size):
      
      if(index==0 and visit[index]==1):
        index+=1
        #This are start vertex
        continue
      
      if(visit[index]>0):
        status=1
        break
          
      index+=1
    
    if(status==1):

      print("Yes")
    else:
      print("No")
      
    
        
    
def main():
  g=Graph(6)
  g.setData() 
  #Connected two node with Edges

  g.addEdge(0,1)
  g.addEdge(0,2)
  g.addEdge(1,3)
  g.addEdge(1,4)

  g.addEdge(2,5)

  g.checkCycle()

  g.addEdge(5,4)

  #Case two
  g.checkCycle()
if __name__=="__main__":
    main()

Output

Adjacency list of vertex  0 :   1   2 
Adjacency list of vertex  1 :   0   3   4 
Adjacency list of vertex  2 :   0   5 
Adjacency list of vertex  3 :   1 
Adjacency list of vertex  4 :   1 
Adjacency list of vertex  5 :   2 
result : No

Adjacency list of vertex  0 :   1   2 
Adjacency list of vertex  1 :   0   3   4 
Adjacency list of vertex  2 :   0   5 
Adjacency list of vertex  3 :   1 
Adjacency list of vertex  4 :   1   5 
Adjacency list of vertex  5 :   2   4 
result : Yes
//C# Graph 
//Detect Cycle in a Undirected Graph
using System;
class AjlistNode
{
	public int key;
	public AjlistNode next;
	public AjlistNode(int key)
	{
		this.key=key;
		this.next=null;
	}
}
class Node
{
	public int data;
	public AjlistNode next;
	public Node(int data)
	{
		this.data=data;
		this.next=null;

	}
}
class MyGraph
{
	//empty array
	public Node[]node= new Node[] {};
	public int size;
	public MyGraph(int size)
	{
		this.size=size;
		node=new Node[size];
	}
	//set initial node value
	public void setData()
	{
		if(node == null)
		{
			Console.WriteLine("\nEmpty Graph");
		}else
		{
			for(int index = 0; index < size; index++)
			{
				// avoid java.lang.nullPointerException
				node[index]=new Node(index); 

			}
		}
	}
	//connect two nodes
	public void connect(int start,int end)
	{
		AjlistNode newEdge=new AjlistNode(end);

		if(node[start].next==null)
		{
			node[start].next=newEdge;
		}else
		{
			AjlistNode temp=node[start].next;

			while(temp.next!=null)
			{
				temp=temp.next;
			}
			temp.next=newEdge;
		}
	}
	//Add edge at the end
	public void addEdge(int start,int end)
	{
		if(start < size && end < size && node != null)
		{
			connect(start,end);
			if(start==end)
			{
				//self loop
				return;
			}
			connect(end,start);
		}else{
			Console.WriteLine("\nEmpty Graph");
		}
	}

	public void printGraph()
	{

		if(size>0 && node!=null)
		{
			for(int index=0;index<size;index++)
			{
				Console.Write("\nAdjacency list of vertex "+index+" :");

				AjlistNode temp=node[index].next;

				while(temp!=null)
				{
					Console.Write(" "+node[temp.key].data);

					temp=temp.next;
				}
			}
		}
	}
	//Detect cycle using DFS
	public void detectCycle(int point,int []visit)
	{

		if(visit[point] >= 1)
		{
			visit[point]=visit[point]+1;
			return;
		}
		visit[point]=1;

		AjlistNode  temp=node[point].next;
		int counter=0;
		while(temp!=null)
		{
			counter++;
			detectCycle(temp.key,visit); 
			temp=temp.next;
		}

		if(counter>0)
		{
			visit[point] = visit[point]-counter;

			if(visit[point]<0)
			{
				visit[point]=-visit[point];
			}
		}
	}
	//method which are manage finding and detecting cycle operation
	public void checkCycle()
	{  

		if(node==null)
		{
			Console.WriteLine("Empty Graph");
			return;
		}

		printGraph();

		//This are storing the information about visiting node status
		int []visit=new int[size];

		for(int index=0;index < size; index++)
		{
			visit[0]=0;
		}
		detectCycle(0,visit); 

		int status=0;

		Console.Write("\nresult : ");

		for(int index=0;index < size; index++)
		{
			
			if(index==0 && visit[index]==1)
			{
				//This are start vertex
				continue;
			}
			if(visit[index]>0)
			{
				status=1;
				break;
			}
		}
		if(status==1)
		{
			Console.WriteLine("Yes");
		}else
		{
			Console.WriteLine("No ");
		}
	}

}
class Program
{

	static void Main(string[] args)
	{
		//create object
		MyGraph g=new MyGraph(6);
		g.setData();
		//Connected two node with Edges



		g.addEdge(0,1);
		g.addEdge(0,2);
		g.addEdge(1,3);
		g.addEdge(1,4);

		g.addEdge(2,5);

		g.checkCycle();

		g.addEdge(5,4);

		//Case two
		g.checkCycle();

	}
}

Output

Adjacency list of vertex 0 : 1 2
Adjacency list of vertex 1 : 0 3 4
Adjacency list of vertex 2 : 0 5
Adjacency list of vertex 3 : 1
Adjacency list of vertex 4 : 1
Adjacency list of vertex 5 : 2
result : No 

Adjacency list of vertex 0 : 1 2
Adjacency list of vertex 1 : 0 3 4
Adjacency list of vertex 2 : 0 5
Adjacency list of vertex 3 : 1
Adjacency list of vertex 4 : 1 5
Adjacency list of vertex 5 : 2 4
result : Yes
<?php 
/*
* PHP Program 
* Detect Cycle in a Directed Graph
*/

class AjlistNode
{
  public $key;
  public $next;
  function __construct($key)
  {
    $this->key=$key;
    $this->next=NULL;
}
}
class Node
{
  public $data;
  public $next;
  function __construct($data)
  {
    $this->data=$data;
    $this->next=NULL;

}
}
class MyGraph
{

    public $node;
    public $size;
    function __construct($size)
    {
        $this->size=$size;
        $this->node=[];  //empty array
    }
    public function setData()
    {
        if($this->size>0)
        {
            for($index=0;$index<$this->size;$index++)
            {
                $this->node[$index]=new Node($index);
            }

        }
    }
    public function connect($start,$end)
    {
        $newEdge=new AjlistNode($end);
        if($this->node[$start]->next==NULL)
        {
            $this->node[$start]->next=$newEdge;
        }
        else
        {

            $temp=$this->node[$start]->next;
            while($temp->next!=NULL)
            {
                $temp=$temp->next;
            }
            $temp->next= $newEdge;
        }
    }
    public function addEdge($start,$end)
    {
        if($this->size > $start && $this->size>$end)
        {
            $this->connect($start,$end);
            if($start==$end)
            {
                //self loop 
                return;
            }
            $this->connect($end,$start);
        }
        else
        {
            echo "\n Invalid node";
        }
    }
    public function printGraph()
    {
        if($this->size>0 && count($this->node)>0 && $this->node!=NULL)
        {
            for($index=0;$index<$this->size;$index++)
            {
                echo ("\nAdjacency list of vertex ".$index." : ");
                $temp=$this->node[$index]->next;
                while($temp!=NULL)
                {
                    echo (" ".$this->node[$temp->key]->data);
                    $temp=$temp->next;
                }
            }
        }
    }

    public function detect_cycle($point,&$visit)
    {

        if($visit[$point] >= 1)
        {

            $visit[$point]=$visit[$point]+1;
            return;
        }
        $visit[$point]=1;

        $temp=$this->node[$point]->next;
        $counter=0;
        while($temp!=null)
        {
            $counter++;
            $this->detect_cycle($temp->key,$visit); 
            $temp=$temp->next;
        }

        if($counter>0)
        {
            $visit[$point] = $visit[$point]-$counter;

            if($visit[$point]<0)
            {
                $visit[$point]=-$visit[$point];
            }
        }
    }
    public function check_cycle()
    {

        if($this->node==null)
        {
            echo ("Empty Graph");
            return;
        }

        $this->printGraph();

        //This are storing the information about visiting node status
        $visit=[];
        
        for($index=0;$index < $this->size; $index++)
        {
         $visit[$index]=0;
     }
     $this->detect_cycle(0,$visit); 

     $test=0;
     $status=0;

     echo ("\nResult : ");

     for($index=0; $index < $this->size; $index++)
     {

        if($index==0 && $visit[$index]==1)
        {
                //This are start vertex
            continue;
        }
        if($visit[$index]>0)
        {
            $status=1;
            break;
        }
    }
    if($status==1)
    {
        echo ("Yes\n");
    }else
    {
        echo ("No\n");
    }
}

}


function main()
{
    //create object
    $g=new MyGraph(6);
    $g->setData();

    //Connected two node with Edges
    $g->addEdge(0,1);
    $g->addEdge(0,2);
    $g->addEdge(1,3);
    $g->addEdge(1,4);

    $g->addEdge(2,5);

    $g->check_cycle();

    $g->addEdge(5,4);

    //Case two
    $g->check_cycle();

}
main();
?>

Output

Adjacency list of vertex 0 :  1 2
Adjacency list of vertex 1 :  0 3 4
Adjacency list of vertex 2 :  0 5
Adjacency list of vertex 3 :  1
Adjacency list of vertex 4 :  1
Adjacency list of vertex 5 :  2
Result : No

Adjacency list of vertex 0 :  1 2
Adjacency list of vertex 1 :  0 3 4
Adjacency list of vertex 2 :  0 5
Adjacency list of vertex 3 :  1
Adjacency list of vertex 4 :  1 5
Adjacency list of vertex 5 :  2 4
Result : Yes


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