We can find shortest path in un-weighted graphs using DFS.

Multiplying every edge weight by a positive constant, does not change the solution to the single-source shortest-paths problem. (i.e., we pick a constant and for every edge ,  weight() changes to weight()).

Adding a constant to every edge weight does not change the solution to the single-source shortest-paths problem. (i.e., we pick a constant and for every edge ,  weight() changes to weight() + ).