t01_y2008 - The University of Sydney MATH2969/2069 Graph...

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The University of Sydney MATH2969/2069 Graph Theory Tutorial 1 (Week 8) 2008 1. Draw a picture of each of the following graphs, and state whether or not it is simple. (a) G 1 = ( V 1 , E 1 ), where V 1 = { a, b, c, d, e } and E 1 = { ab, bc, ac, ad, de } . (b) G 2 = ( V 2 , E 2 ), where V 2 = { P, Q, R, S, T } and E 2 = { PQ, PR, PS, PT, TR, PR } . (c) G 3 = ( V 3 , E 3 ), where V 3 = { v 1 , v 2 , v 3 , v 4 , v 5 } and E 3 = { v 1 v 1 , v 1 v 2 , v 2 v 3 , v 3 v 4 , v 5 v 4 , v 4 v 5 } . 2. For each of the following graphs write down the number of vertices, the number of edges and the degree sequence. Verify the hand-shaking lemma in each case. ( i ) ( ii ) 3. A sequence d = ( d 1 , d 2 , . . ., d n ) is graphic if there is a simple graph with degree sequence d . Determine whether or not the following sequences are graphic. If the sequence is graphic, draw a corresponding graph. (a) (2 , 3 , 3 , 4 , 4 , 5) (b) (2 , 3 , 4 , 4 , 5) (c) (1 , 1 , 1 , 1 , 4) (d) (1 , 3 , 3 , 3) (e) (1 , 2 , 2
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t01_y2008 - The University of Sydney MATH2969/2069 Graph...

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