**Depth First Search:**

Depth-first search starts visiting vertices of a graph at an arbitrary vertex by marking it as having been visited. On each iteration, the algorithm proceeds to an unvisited vertex that is adjacent to the one it is currently in. This process continues until a vertex with no adjacent unvisited vertices is encountered. At a dead end, the algorithm backs up one edge to the vertex it came from and tries to continue visiting unvisited vertices from there. The algorithm eventually halts after backing up to the starting vertex, with the latter being a dead end.

**Complexity:** For the adjacency matrix representation, the traversal time efficiency is in Θ(|V|2) and for the adjacency linked list representation, it is in Θ(|V|+|E|), where |V| and |E| are the number of graph‟s vertices and edges respectively.

` ````
```#include
#include
int a[20][20],reach[20],n;
void dfs(int v)
{
int i;
reach[v]=1;
for(i=1;i<=n;i++)
if(a[v][i] && !reach[i])
{
printf("\n %d->%d",v,i);
dfs(i);
}
}
void main()
{
int i,j,count=0;
clrscr();
printf("\n Enter number of vertices:");
scanf("%d",&n);
for(i=1;i<=n;i++)
{
reach[i]=0;
for(j=1;j<=n;j++)
a[i][j]=0;
}
printf("\n Enter the adjacency matrix:\n");
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
scanf("%d",&a[i][j]);
dfs(1);
printf("\n");
for(i=1;i<=n;i++)
{
if(reach[i])
count++;
}
if(count==n)
printf("\n Graph is connected");
else
printf("\n Graph is not connected");
getch();
}