Q3. - Geometry

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.

Step-by-Step Solution

Answer

The number of odd and even vertices is $2$ and $6.$

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, by observing, the total number of vertices $=8.$

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.

Hence, the number of odd vertices $=2.$

                   The number of even vertices $=6.$