how to visit each point in directed graph

Question

In Prolog, how can I implement graph algorithm in order to find all path in order to implement travel salesman problem in directed graph ?

example :

Answer 1

I placed some comment that explain what the code does...

% your directed graph
edge(x, y).
edge(y, t).
edge(t, z).
edge(y, z).
edge(x, z).

% get a path from start to end
path(Start, End, Path) :-
    path(Start, End, [Start], Path).

% when target reached, reverse the visited list
path(End, End, RPath, Path) :-
    reverse(RPath, Path).

% take non deterministically an edge, check if already visited before use
path(Start, End, Visited, Path) :-
    edge(Start, Next),
    \+ memberchk(Next, Visited),
    path(Next, End, [Next|Visited], Path).

test:

?- path(x,z,P).
P = [x, y, t, z] ;
P = [x, y, z] ;
P = [x, z] ;
false.

Answer 2

Keep a list of nodes you have already visited. In each step, check if the endpoint of the edge exists in the list or not.