Chapter 13, Problem 1RE

In Exercises 1 and 2, create a graph with the given properties.

1. Create a graph with four even vertices, two odd vertices, a bridge, and a loop.

To determine

To sketch: A graph with four even vertices, two odd vertices, a bridge and a loop.

Explanation of Solution

One of the possible graph with four even vertices, two odd vertices, a bridge and a loop is shown below in Figure 1.

From Figure 1, it can be observed that the graph has only six vertices and eight edges.

Here the vertices A, E, F, D are even vertices and the vertices B and C are odd vertices.

That is, there are four even vertices and two odd vertices.

Recall that, a bridge is an edge if it is removed from the graph then graph will becomes disconnected.

If the edge BC is removed, the graph will becomes disconnected.

Therefore, BC is a bridge of the graph; also it is the only one bridge of this graph.

Also the graph has a loop at the vertex D.