In case we have two shortest paths, it seems that the one with the letter occuring earlier in the alphabet is chosen. For depth-first and breadth-first search, such a hint is given:
"Nehmen Sie an, dass der Algorithmus die Kanten in der alphabetischen Reihenfolge ihrer Zielknoten durchläuft"
For the Dijkstra task, such a hint would clarify how to get to a unique solution.