# Answered Essay: Modify the DFs algorithm to determine whether or not the input graph is a connected grap

Modify the DFs algorithm to determine whether or not the input graph is a connected graph. DEPTH FIRST SEARCH Input: A labelled graph G = (V , E) (not necessarily connected) Output: A forest F (a set of edges) and the order in which the vertices were traversed (DFI). Method: Label each vertex v with DFI(v), which is the order in which it is traversed, until all vertices have be reached. Uses recursion. i: = 1 F: = for all v elementof V do DFI (v): = 0 while for some u, DFI (u) = 0 do begin DFS(u) end Procedure DFS(v) DFI (v): = i i: = i + 1 for all v’ elementof A(v) do begin if DFI (v’) = 0 then begin F: = F Union { (v, v’)} DFS(v’) end end

In DFS we traverse all nodes ot graph. When we traverse we insert value in DFI array either this node is visited or not. After calling DFS we will check in DFI for all nodes if any of node is not visited then we return false and we can say graph is not connected.

1.i:=1

2.F:=0

3.for all v $\varepsilon$ V do DFI(v):=0

4.while for some u, DFI(u) = 0 do begin

5. DFS(u)

6.end

7.if connected()

8. print “connected”

9.else

10. print “not connected”

procedure connected()

1.for all nodes u:

2. if DFI is 0

3. return false

4.return true

procedure DFS(v)

1.DFI(v): = i

2.i:= i+1

3.for all v’ $\varepsilon$ A(v) do begin

4. if DFI(v’) = 0 then begin

5. F: = F $\bigcup$ {(v,v’)}

6. DFS(v’)

7. end

8.end

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