Unformatted text preview: both AB and AG are in. So Ji is ABDF EGA as shown on the right above. 5. (a) [BB] Yes, it is Hamiltonian: ABDGEA is a Hamiltonian cycle. (b) Any Hamiltonian graph has a Hamiltonian path; in the graph here, ABDGE is a Hamiltonian path, for instance. (c) [BB] The graph is not Eulerian. Vertices A and E have odd degree. (d) The trail indicated is Eulerian. E B(Jf"~C D 6. (a) Yes, it is possible. Here is a Hamiltonian cycle for the knight. 5 64 25 28 41 44 53 46 24 27 4 63 52 47 40 43 CD 6 17 26 29 42 45 54 18 23 62 3 48 51 34 39 7 2 19 16 35 30 55 50 22 13 10 61 58 49 38 33 11 8 15 20 31 36 59 56 14 21 12 9 60 57 32 37...
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 Summer '10
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 Graph Theory, Prime number, Glossary of graph theory, hamiltonian cycle, Graph theory objects, Eulerian path, Ji

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