PROBLEM $2$ Refer to the undirected graph provided below: Figure $6$: An undirected graph has $9$ vertices. $6$ vertices form a hexagon, which is tilted upward to the right. Starting from the leftmost vertex, moving clockwise, the vertices forming the hexagon shape are: D$,$ A$,$ B$,$ E$,$ I, and F$.$ Vertex H is above and to the right of vertex B$.$ Vertex G is the rightmost vertex, below vertex H and above vertex E$.$ Vertex C is the bottommost vertex, a little to the right of vertex E$.$ Undirected edges, line segments, are between the following vertices: A and D; A and B; B and F; B and H; H and G; G and E; B and E; A and E; E and I; I and C; I and F; and F and D$.($i$)$ Whati isi thei maximumi lengthi ofi ai pathi ini thei graph?i Givei ani examplei ofi ai pathi ofi thati length.