Discrete Mathematics with Graph Theory (3rd Edition) 254

Discrete Mathematics with Graph Theory (3rd Edition) 254 -...

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252 Solutions to Exercises 13. [BB] Consider the graph in which the vertices correspond to the people at the party and an edge between vertices indicates that the corresponding people shook hands. The degree of a vertex in this graph is the number of hands that person shook. The result is an immediate consequence of Corollary 9.2.6. 14. Only graphs (ii), (iv) and (v) are subgraphs of the graph in Fig. 9.21, as shown. 15. Yes for (a) [BB] and (c), as indicated. A B1~r D 1 4 D 8 5 (ii) (c) 1 4 1 4
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Unformatted text preview: IZ1 B 8 5 8 5 (v) (vi) A NrO: 1 2 3 B (b) No. The graph on the left contains two vertices of degree 3 while the one on the right has just one vertex of degree 2': 3. (d) No. In the graph on the right, every two triangles share a vertex. v 16. (a) [BD] ~ o g" {e} g" {u} (c) u u (d)H 1> I ~ g" {e} 17. (a) [BB] Degree ofvl is 1; degree ofv2 is 3; degree ofv3 is 4; degree ofv4 is 2. (b) [BB] No. The maximum degree of a vertex in a graph with four vertices is 3. (Loops are not allowed in graphs.)...
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