D C B E F A Consider the graph given above. Add an edge so the resulting graph has an Euler path (without repeating an existing edge). Now give an Euler path through the graph with this new edge by listing the vertices in the order visited.

QUESTION 20 Choose the true statement for the following graph. A B D E Oa. The graph has an Euler circuit. Ob. The graph has an Euler path. Oc. The graph has neither an Euler circuit nor an Euler path. Od. The graph has both an Euler circuit and an Euler path.

For each graph below, find an Euler circuit in the graph or explain why the graph does not have an Euler circuit. (a) Figure 9: An undirected graph has 6 vertices, a through f. 5 vertices are in the form of a regular pentagon, rotated 90 degrees clockwise. IHence, the top verter becomes the rightmost verter. From the bottom left verter, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. Verter d is above verter e, below and to the right of vertex c. Undirected edges, line segments, are between the following vertices: b and e; b and a; b and f; b and e; a and e; a and d; a and f; e and d; e and f; d and e; and d and f. (b) g Figure 10: An undirected graph has 7 vertices, a through g. 5 vertices are in the form of a regular pentagon, rotated 90 degrees clockwise. Ilence, the top verter becomes the rightmost verter. From the bottom left verter, moving clockwise, the vertices and f. Verter d is above vertex e, below and to the right of verter e. Verter g…

Does the bipartite graph of K5, has a Hamilton path or is it Hamiltonian? Explain why it is a Hamilton path or Hamiltonian.

what type of the path a-c-d-e-b-a shows on Graph 3? a. Hamiltonian b. Euler path c. Euler circuit d. Hamiltonian and Eulerian

Find a Hamilton path for each graph below. Hamilton path for Ki: Hamilton path for Kg Hamilton path for Kg:

(c) For cach graph below, find an Euler trail in the graph or explain why the graph does not have an Euler trail. (Hint: One way to find an Euler trail is to add an cdge between two vertices with odd degree, find an Euler circuit in the resulting graph, and then delete the added edge from the circuit.) (i) Figure 11: An undirected graph has 6 vertices, a through f. 5 vertices are in the form of a regular pentagon, rotated 90 degrees clockwise. Hence, the top vertez becomes the rightmost vertez. From the bottom left vertez, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. Vertez d is above vertez e, below and to the right of vertez c. Undirected edges, line segments, are between the following vertices: a and b; a and e; a and d; a and f; b and f; b and e; e and d; e and f; d and e; and d and f.