Question

Determine whether the given simple graph is orientable.

Short answer

The graph is non-orientable due to the edge cut of {b, c}.

Step-by-step solution

Concept/Significance of orientation of graph

An undirected simple graph's orientation is the assignment of directions to its edges, resulting in a highly linked directed graph.

Determination of whether the simple graph is orientable

There can be no path in the resultant directed graph from c to bthat orients it from b to c. Similarly, there can be no path in the resultant directed graph from b to cthat can orient it from c to b.

Because of the cut edge {b, c}, the graph is non-orientable.

Thus, the graph is non-orientable due to the edge cut of {b, c}.