Question

Find the number of odd and even vertices in each network. Imagine travelling each network to see if it can be traced without backtracking.

Short answer

The number of odd and even vertices is $0$ and $6.$

Step-by-step solution

Step 1. Given information:

The given figure is as follows:

Step 2. Concept use.

A vertex with odd number of edges attached to it is called odd vertex and a vertex with even number of edges attached to it is called even vertex.

Step 3.  Applying the concept.    

In the given network, total number of vertices $=6.$

A vertex with odd number of edges attached to it is called odd vertex and a vertex with even number of edges attached to it is called even vertex.

By observing the network, its clear that all nodes are having even number of edges attached to it.

Hence, the number of odd vertices $=0.$

The number of even vertices $=6.$