WUCT121 Discrete Mathematics Graphs Tutorial Exercises Solutions

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e 2 v 1 v 2 e 4 v 3 There are other possibilities. Question4 (c) Either write down a path with the specified properties, or explain why no such path exists. (i) A path of length 5 from v 1 to v 2 . One possible: v 1 , e1 , v1, e2 , v1, e1 , v1, e2 , v1, e5 , v2 (ii) A path of length 3 from v 1 to v 3. One possible: v 1 , e2 , v1, e5 , v2 , e3, v3 (a) Draw all spanning trees for K 3 . v 1 K 3 e 3 e 1 v 3 e 2 v 2 v 1 v 1 v 1 e 1 e 3 e 3 e 1 v 3 e 2 v 2 v 3 e 2 v 2 v 3 v 2 WUCT121 Graphs: Tutorial Exercise Solutions 6
(b) Draw 8 different spanning trees for K 4 . It can be shown that there are spanning trees for K n . Can you write down 16 spanning trees for K 4 n−2 n K 4 v 1 e 4 v 4 e 5 e 6 e 1 e 3 v 2 e 2 v 3 v 1 e 1 v 2 v 1 v 2 v 1 e 1 v 2 v 1 e 1 v 2 e 2 e 4 e 2 e 4 e 4 e 2 v 4 v 1 v 4 e 6 e 3 e 1 e 3 v 3 v 2 v 3 v 4 v 1 v 4 e 5 e 3 e 1 e 3 v 3 v 2 v 3 v 4 v 1 e 4 v 4 e 6 e 3 v 3 v 2 e 2 v 3 v 4 v 1 e 4 v 4 e 5 v 3 v 2 e 2 v 3 v 1 v 4 v 1 e 4 v 4 e 5 e 6 e 5 e 1 e 1 v 2 v 3 v 2 v 3 v 1 v 4 v 1 v 4 e 5 e 6 e 6 e 3 e 1 v 2 v 3 v 2 e 2 v 3 v 1 e 4 v 4 v 1 v 4 e 5 e 6 e 5 e 3 v 2 v 3 v 2 e 2 v 3 v 1 v 4 v 1 e 4 v 4 e 5 e 6 e 6 e 3 v 2 e 2 v 3 v 2 v 3 WUCT121 Graphs: Tutorial Exercise Solutions 7
Page 1 and 2: WUCT121 Discrete Mathematics Graphs
Page 3 and 4: Question2 Either draw a graph with
Page 5: Question3 Let G = { V , E} be the g
Page 9: WUCT121 Graphs: Tutorial Exercise S

WUCT121 Discrete Mathematics Graphs Tutorial Exercises Solutions

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