Chapter 9.1, Problem 4E

a.

To determine

To find: Whether a vertex is even or odd.

Answer to Problem 4E

The vertex is even.

Explanation of Solution

The vertex will be even because as it is given in the problem that the vertex is not start or end of the journey via network then it is necessary pass it in another way, if it is coming in one way.

  

b.

To determine

To find: Whether both the vertices are even or odd.

Answer to Problem 4E

Yes.

Explanation of Solution

Both the vertices can be even or odd but it should be kept in mind either both the vertices will be even or both the vertices will be odd. Therefore, there can be two cases related to it.

Case I:- If vertices have same start and end points then both the vertices will be even.

Case II:-If vertices have different start and end points then both the vertices will be odd.

c.

To determine

To find: Whether only one of the start and finish vertices can be odd or not.

Answer to Problem 4E

No

Explanation of Solution

Only one of the start and finish vertices cannot be odd. This is because of the other vertex which is even. As that vertex is even, it is made to enter then it have to leave also. This makes it sure that other vertex should be neither start nor the end point.