Question

Determine whether the given simple graph is orientable.

Short answer

No. The graph is not orientable due to the edge cut\(\left\{ {c,\;d} \right\}.\)

Step-by-step solution

Concept/Significance of undirected graph

An undirected graph is a graph in which the edges are bidirectional, which means that each edge may be visited in both directions, indicating that the connection is two-way.

Determination of whether the simple graph is orientable

Whenever the edges of an undirected simple graph are assigned orientations such that the resultant graph is strongly linked, the graph is orientable. Because there is a cut edge\(\left\{ {c,\;d} \right\}\)in the current graph, assigning directions to its edges is impossible, making it weakly connected. So, it is not orientable.

Thus, the graph is non-orientable due to the edge cut of\(\left\{ {c,\;d} \right\}.\)