If the simple graph G has 20 vertices and 55 edges, how many edges does its complement G' has?

Sure, here are the steps to find the number of edges in the complement of a graph:

1. First, we need to find the maximum number of edges in a simple graph with 20 vertices. This can be calculated using the formula n(n-1)/2, where n is the number of vertices. So, the maximum number of edges is 20*(20-1)/2 = 190.

2. The complement of a graph G is formed by using the same vertices of G and adding edges where there were none in G, and removing edges where there were in G. So, the number of edges in the complement of G is the maximum number of edges minus the number of edges in G.

3. Therefore, the number of edges in the complement of G, denoted as G', is 190 - 55 = 135. So, G' has 135 edges.