# C Program to find whether an Undirected Graph is Cyclic or not

By | 30.06.2017

## Find whether an Undirected Graph is Cyclic or not

Write a C Program to find whether an Undirected Graph is Cyclic or not. Here’s simple Program to find whether an Undirected Graph is Cyclic or not in C Programming Language.

## Depth First Search (DFS)

Depth First Search (DFS) algorithm traverses a graph in a depthward motion and uses a stack to remember to get the next vertex to start a search, when a dead end occurs in any iteration.

It employs the following rules.

• Rule 1 − Visit the adjacent unvisited vertex. Mark it as visited. Display it. Push it in a stack.
• Rule 2 − If no adjacent vertex is found, pop up a vertex from the stack. (It will pop up all the vertices from the stack, which do not have adjacent vertices.)
• Rule 3 − Repeat Rule 1 and Rule 2 until the stack is empty.

We shall not see the implementation of Depth First Traversal (or Depth First Search) in C programming language

Also Read : : C Program for Traversing Directed Graph through DFS and classifying all edges

Below is the source code for C Program to find whether an Undirected Graph is Cyclic or not in output which is successfully compiled and run on Windows System to produce desired output as shown below :

### SOURCE CODE : :

```/*  C Program to find whether an Undirected Graph is Cyclic or not  */

#include<stdio.h>
#include<stdlib.h>

#define MAX 100
#define NIL -1

#define initial 1
#define visited 2
#define finished 3

int n;    /* Denotes number of vertices in the graph */

int state[MAX];
int predecessor[MAX];

void create_graph();
void DF_Traversal();
void DFS(int v);

int main()
{
create_graph();
DF_Traversal();
return 0;
}/*End of main()*/

void DF_Traversal()
{
int v;
for(v=0; v<n; v++)
{
state[v] = initial;
predecessor[v] = NIL;
}
DFS(0); /*start from vertex 0*/
for(v=0; v<n; v++)
{
if(state[v] == initial)
DFS(v);
}
printf("\nGraph is acyclic\n");
}/*End of DF_Traversal()*/

void DFS(int v)
{
int i;
state[v] = visited;
for(i=0; i<n; i++)
{
if( adj[v][i] == 1 && predecessor[v]!=i )
{
if( state[i] == initial)
{
predecessor[i]=v;
DFS(i);
}
else if(state[i] == visited )
{
printf("\nBack edge (%d,%d) detected \n", v, i);
printf("\nGraph is cyclic\n");
exit(1);
}
}
}
state[v] = finished;
}/*End of DFS()*/

void create_graph()
{
int i,max_edges,origin,destin;

printf("\nEnter number of vertices : ");
scanf("%d",&n);
max_edges = n*(n-1)/2;

for(i=1;i<=max_edges;i++)
{
printf("\nEnter edge %d( -1 -1 to quit ) : ",i);
scanf("%d %d",&origin,&destin);

if( (origin == -1) && (destin == -1) )
break;

if( origin >= n || destin >= n || origin<0 || destin<0)
{
printf("\nInvalid edge!\n");
i--;
}
else
{
}
}/*End of for*/
}/*End of create_graph()*/```

### OUTPUT : :

```/*  C Program to find whether an Undirected Graph is Cyclic or not  */

Enter number of vertices : 5

Enter edge 1( -1 -1 to quit ) : 0 1

Enter edge 2( -1 -1 to quit ) : 0 2

Enter edge 3( -1 -1 to quit ) : 0 3

Enter edge 4( -1 -1 to quit ) : 0 4

Enter edge 5( -1 -1 to quit ) : 1 0

Enter edge 6( -1 -1 to quit ) : 2 4

Enter edge 7( -1 -1 to quit ) : 3 4

Enter edge 8( -1 -1 to quit ) : -1 -1

Back edge (4,0) detected

Graph is cyclic

Process returned 1```

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