H is called a wheel and is the simplest type of Halin graph." The graph of a triangular prism is also a Halin graph: it can be drawn so that one of its rectangular faces is the exterior cycle, and the remaining edges form a tree with four leaves, two interior vertices, and five edges.See , Prop. 4.3, p. 254, which identifies the triangular prism as the unique graph with exactly three cycles that can be the outer cycle of a realization as a Halin graph.
