Question: Question 1 (3 points) Q4A. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {{a,

Question 1 (3 points) Q4A. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {{a, b}, {a, c], {a, d}, {a, f}, {b, c], {b, e}, {b, f}, {c, d}, {c, f], {d, e], {d, f}} Explain why the graph either does or does not have an Euler circuit. C d b e a All vertices have even degree. Therefore, the graph does have an Euler circuit. Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have odd degree. Therefore, the graph does not have an Euler circuit. Two vertices (b and f) have odd degree. Therefore, the graph does not have an Euler circuit.Question 2 (3 points) Q5D. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c], {a, f}, {b, c], {b, f}, {c, d}, {c, g], {d, e], {d, f], {f, g}} Explain why the graph either does or does not have an Euler trail. e a g All vertices have odd degree. Therefore, the graph does not have an Euler trail. Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have an Euler trail. Exactly two vertices (b and e) have odd degree. Therefore, the graph does have an Euler trail. All vertices have even degree. Therefore, the graph does not have an Euler trail. Exactly two vertices (c and e) have odd degree. Therefore, the graph does have an Euler trail.Question 3 (3 points) Q6B. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c], {a, f}, {b, c], {b, f}, {c, d}, {c, g], {d, e], {d, f}, {f, g}} d b e a g Which of the following are examples of trails within the graph? (Select all that apply.) O ( ( (Question 4 (3 points) Q9D. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {{a, b}, {a, c], fa, d}, fa, f}, {b, c], {b, e], {b, f}, {c, d}, {c, f], {d, e], {d, f}} C b e a Which of the following is true about Hamiltonian cycles and paths for the graph? The graph has a Hamiltonian cycle and a Hamiltonian path. The graph has a Hamiltonian path but not a Hamiltonian cycle. The graph has a Hamiltonian cycle but not a Hamiltonian path. The graph has neither a Hamiltonian path nor a Hamiltonian cycle.Question 5 (3 points) Q10C. Consider the graph with the following vertices and edges: V = {a. b, c, d, e, f} E = {{a, b}, {a. c}, {3, d}, {a, f}, {b, e}. {b, f}, {c, d}, {d, 6}, id, f}} Which of the following are examples of circuits within the graph? (Select all that apply.)

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