Question

Asked May 13, 2019

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

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 2* ^{n}*.

We already obtained that, the number of edges of a graph with *n* vertices is _{n}P_{2}.

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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