Q1. - 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 $4$ and $1.$ 

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.

By observing the given network, four nodes are having three lines connected to it and     one node with four lines connected to it.

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 $=4$.

The number of odd vertices $=1$.