CMSC 250 Fall 2001 Homework 14 solutions

1. Directed Graph

   

2. A connected graph

   

3. A Simple graph

   

4. A connected 3-partite graph

   

5. 1. 

   2. Vertex A(in degree:3,out degree:4)

      Vertex B(in degree:2,out degree:4)

      Vertex C(in degree:6,out degree:4)

      Vertex D(in degree:2,out degree:4)

      Vertex E(in degree:4,out degree:2)

      Vertex F(in degree:5,out degree:4)

      Vertex G(in degree:2,out degree:2)

      Vertex H(in degree:4,out degree:4)

   3. 

   4. Degree of: Vertex A=7

      Vertex B=6

      Vertex C=10

      Vertex D=6

      Vertex E=6

      Vertex F=9

      Vertex G=4

      Vertex H=8

   5. 

   6. Degree of: Vertex A=4

      Vertex B=3

      Vertex C=5

      Vertex D=3

      Vertex E=4

      Vertex F=5

      Vertex G=3

      Vertex H=5

6. A weakly connected directed graph with 4 vertices

   

7. A connected undirected simple graph on 8 vertices such that every vertex has an odd degree of at atleast 3.

   

8. 1. Not possible. There are vertices of odd degree.

   2. Example: $1a2d3i4g6h5c$

   3. Example: $2d3f6b1b6h5$

   4. Example: $1a2d3i4g6h5j4g6b1$

   5. $3i4g6h5c1b6e2d3$

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