The number of edges can be calculated from the number of vertices.
- <em>There are 14 vertices for 105 edges</em>
- <em>There are 200 vertices for 19900 edges</em>
The variable N is used to always represent the number of vertices.
So, we represent the edges as:
<u />
<u>(a) The value of N for 105 edges</u>
The relationship between N and E is:
Substitute 105 for E
Multiply through by 2
Rewrite as:
Expand
Factorize
Factor out N + 14
Solve for N
or
The number of vertices (N) cannot be negative. So:
<u>(b) The value of N for 19900 edges</u>
We have:
Substitute 19900 for E
Multiply through by 2
Rewrite as:
Expand
Factorize
Factor out N + 199
Solve for N
or
The number of vertices (N) cannot be negative. So:
<em>Hence, there are 200 vertices for 19900 edges</em>
Read more about vertices and edges at:
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