# How many possible graphs can be created on 5 distinct vertices?

Question

How many possible graphs can be created on 5 distinct vertices?

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Step 1

Consider a graph of n vertices.

The line connecting any two vertices of a graph is called as an edge of the graph.

The number of edges of a graph with n vertices is,

Step 2

Now, we have to obtain the total number of graphs can be formed n(n-1)/2 this edges.

If the cardinality of a set is n, then the number of subsets can be formed is 2n.

We already obtained that, the number of edges of a graph with n vertices is nP2.

Therefore, the number of graphs can be formed with n vertices is,

Step 3

Given that, the number of vertices is 5.

Then, the possible...

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### Math 