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 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.
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Chapter 13 Solutions
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