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) What is the maximum length of a path in the graph? Give an example of a path of that length. (ii) What is the maximum length of a cycle in the graph? Give an example of a cycle of that length. (iii) Give an example of an open walk of length five in the graph that is a trail but not a path. (iv) Give an example of a closed walk of length four in the graph that is not a circuit. (v) Give an example of a circuit of length zero in the graph.
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) What is the maximum length of a path in the graph? Give an example of a path of that length.
(ii) What is the maximum length of a cycle in the graph? Give an example of a cycle of that length.
(iii) Give an example of an open walk of length five in the graph that is a trail but not a path.
(iv) Give an example of a closed walk of length four in the graph that is not a circuit.
(v) Give an example of a circuit of length zero in the graph.
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(iv) Give an example of a closed walk of length four in the graph that is not a
circuit.
(v) Give an example of a circuit of length zero in the graph.
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