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f2006Solns12

# f2006Solns12 - ECE 190 Fall 2004 Assignment 12 Solutions...

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ECE 190 — Fall, 2004 Assignment 12 Solutions Questions for Week of November 27 to December 1 Section 11.5 8 See text. 9 See text. 10 See text. 11 See text. 12 See text. 15 One such graph is ••••••• ................................................ . ............................................... 20 One such graph is ••• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Section 11.6 1 See text. 7 See text. Questions on Material not in Epp 1 The graph is not planar. If it is redrawn with a between c and e as well as d between f and b , we can see that the graph is K 3 , 3 which we know is not planar. ± ± ± ± ± ± ± ± ² ² ² ³ ³ ³ ³ ³ ³ ³ ³ ³ ´ ´ ´ ´ ´ ´ ´ ´ ´ µ µ µ µ µ µ ² ² ² ± ± a b c d e f 2 Since each of the six vertices is of degree 4, the total degree of the graph is 24. By the handshaking theorem, the total number of edges, e is 12. Substituting e = 12 and v =6in the formula v - e + f = 2 gives

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