In the following graph, find a Hamiltonian path and prove that no Hamiltonian cycle exists g 90 a h d
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- What does Dirac’s Theorem state? Explain how it guarantees that the graph is HamiltonianWhich of the graph/s above contains an Euler Trail? Which of the graph/s above is/are Eulerian? Which of the graph/s above is/are Hamiltonian?A wheel graph W₁, n ≥ 4 is the graph made from the cycle Cn-1 by adding an additional vertex vn (in the center of the cycle) and additional edges connecting Vn to each vertex of Cn-1. Describe the graph Wn and prove that Wn is Hamiltonian.
- The picture on the left is that of an icosahedron, a solid object whose faces consist of 20 congruent equilateral triangles. By stretching the base triangle and flattening, the icosahedron determines a graph in the plane (as shown on the right side of the figure). Find a Hamiltonian cycle in this graph.Prove that every hamiltonian graph contains no cut-vertex.8. Let G be the graph below. (а) Does G has the Hamiltonian path? (b) Does G has the Hamiltonian cycle?
- 16. Determine whether or not the graph shown is Hamiltonian. If yes explain why and produce the Hamiltonian cycle, if no explain why not. Determine also whether or not the graph has a Hamiltonian path. If yes produce the Hamiltonian path or explain why no such path exists. I K F В E DUse Dirac's Theorem to verify that the graph is hamiltonian and then find a hamiltonian circuit.Answer the following questions for the graph G below: (1) Find a vertex cover for G. (2) Is V={a, c} a vertex cover for G? Why? (3) Find a maximum clique in G. (4) Does G have a clique of size 4? Why? (5) Does G have a Hamiltonian cycle? If yes, find one. If no, explain why. a b. d.