Tutorial 6 - Hamiltonian Cycle I II 7 Write the adjacency...

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DCS5028 DISCRETE STRUCTURES TUTORIAL 6 1 CHAPTER 6: Graphs 1. Find a path of minimum length from v to w in the graph below that passes through each vertex exactly one time. a 4 2 8 3 6 d c b 5 6 4 9 e 12 (i) v = b, w = e (ii) v = c, w = d (iii) v = a, w = b 2. For questions (i-iii), tell whether the given path in the graph below is a simple path, a cycle and a simple cycle. (i) e, d, c, b (ii) a,d,c,d,e a b c d e
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DCS5028 DISCRETE STRUCTURES TUTORIAL 6 2 (iii)b,c,d,e,b,b 3. Find the degree of each vertex for the following graph 4. Decide whether the graphs below have an Euler Cycle. If yes, exhibit one. (i) (ii) v3 v6 v9 v1 v7 v4 v8 v10 v2 v5 v6 v3 v9 v1 v7 v4 v8 v10 v2 v5 v1 v2 v3 v4 v5
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DCS5028 DISCRETE STRUCTURES TUTORIAL 6 3 5. Show that the graph below contains NO Hamiltonian Cycle. 6. Determine whether or not the graph below contains a Hamiltonian Cycle. If there is a Hamiltonian Cycle, exhibit it. Otherwise, give an argument that shows there is no
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Unformatted text preview: Hamiltonian Cycle. I. II. 7. Write the adjacency matrix and the incidence matrix for the graph below: a b d e c f g h i j a b c d e f g e 6 e 1 e 2 e 3 e 4 e 5 v 1 v 2 v 3 v 5 v 4 DCS5028 DISCRETE STRUCTURES TUTORIAL 6 4 I. II. 8. Draw the graph represented by the adjacency matrix below: a b c d e a 0 1 0 0 0 b 1 0 0 0 0 c 0 0 0 1 1 d 0 0 1 0 1 e 0 0 1 1 2 x1 a b x11 x2 x5 x4 c x3 g x6 d x7 x8 e x9 x10 f e7 e8 e2 e4 e1 e3 e5 e6 v2 v3 v4 v5 v1 v6 v7 DCS5028 DISCRETE STRUCTURES TUTORIAL 6 5 9. Prove that graphs G1 and G2 below are isomorphic. 10. Show that the graph below is planar by redrawing it so that no edges cross. I. II h i g f e d v u z y x w M N b a c e d c d a b e f DCS5028 DISCRETE STRUCTURES TUTORIAL 6 6 d a f e b 11. State whether the graph below is a bipartite graph. If the graph is bipartite, specify the disjoint vertex sets. I. II. v1 v2 v3 v4 v5 c...
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