Question

Determine whether the given simple graph is orientable.

Short answer

Yes, the graph is orientable due to the clockwise direction of the paths.

Step-by-step solution

Concept/Significance of orientation of undirected graph

An undirected simple graph's orientation is the assignment of directions to its edges, resulting in a highly linked directed graph. An undirected graph is referred to be orientable when it has an orientation.

Determination of whether the simple graph is orientable

To be firmly linked, each pair of vertices (a, b), (b, c), (c, d), (d, a), (c, e), (e, f), (f, c), (c, g), (g, h), and (h, c) must be able to go from one vertex to the next and back. By allocating the directions of each cycle to follow the same route around, the cycles share a single vertex in a clockwise manner.

Thus, the graph is orientable due to clockwise direction of the paths.