starts with A, Now you have choice of B and D, according to Tie break rule B is choosen
Now you are at B, you have choice of E only,
Now you are at E, you have choice of C and G, according to Tie break rule C is choosen
Now you are at C, you have choice of A and G, but note that A already visited, therefore you have choice of G only.
Now you are at G, you can't go ===> control return to C
Now you are at C, you can't go (due to all adjacent vertices completed ) ===> control return to E
Now you are at E, you can't go (due to all adjacent vertices completed ) ===> control return to B
Now you are at B, you can't go (due to all adjacent vertices completed ) ===> control return to A
Now you are at A, you have choice of D only,
Now you are at D, you have choice of F only,
Now you are at F, you can't go (due to all adjacent vertices completed ) ===> control return to D
Now you are at D, you can't go (due to all adjacent vertices completed ) ===> control return to A
Now you are at F, you can't go (due to all adjacent vertices completed ) ===> DFS travel over.
Now your DFS tree look like as
Note that there is no difference between right and left ( As we did in Binary trees )
Now take every edge of Graph G
(A,B) ===> part of DFS tree ===> it is Tree Edge
(A,D) ===> part of DFS tree ===> it is Tree Edge
(B,E) ===> part of DFS tree ===> it is Tree Edge
(E,C) ===> part of DFS tree ===> it is Tree Edge
(E,G) ===> E is a Ancestor of G ===> it is Forward Edge
(C,A) ===> C is a Descendent of A ===> it is Backward Edge
(C,G) ===> part of DFS tree ===> it is Tree Edge
(D,F) ===> part of DFS tree ===> it is Tree Edge
(F,C) ===> F is neither Ancestor nor Descendent of C ===> it is Cross Edge
(F,G) ===> F is neither Ancestor nor Descendent of G ===> it is Cross Edge
totally, 6 Tree Edges ( due to 7 vertices ) + 1 Forward Edge + 1 Backward Edge + 2 Cross Edges exist in this graph G
For Directed Graph:-
total edges = Tree edges + Front Edges + Back Edges + Cross Edges
For Undirected Graph:-
total edges = Tree edges + Front Edges ( or Back Edges )
https://gateoverflow.in/279686/data-structure-doubt?show=279829#c279829