Discrete math Each digraph G V E has an associated undirect

Each digraph G = (V, E) has an associated (undirected) graph G\' = (V\', E\') where V\' = V and each directed edge (u,v) epsilon E becomes an (undirected) edge {u, v} epsilon E\': (Thus, G\' is obtained from G by removing the directional arrows from the edges of G.) If G is a simple digraph, must the associated graph G\' be a simple graph? Give a proof or counterexample.

Solution

Yes,

G\' is a simple graph as we can see that only the directed edges become undirected. So there are no edges add to make the graph non-planar or not simpler, so we have G\' as a simple graph.