Chapter 4, Problem 1SE

To determine

The complement of the given multi graph.

Explanation of Solution

Let G be a given graph.

Label the vertices of the given graph as follows.

The complement of the graph above is can be constructed as below.

As per the definition given, the vertices are retained as it is.

The vertices A and B does not have an edge in Figure 1 and hence, in Figure 2, there is an edge in between A and B.

Similarly proceeding, the complement of the graph G is obtained as shown below in Figure 2.

Figure 2 is the complement graph of G.