Question

How many edges does a \({\rm{50}}\)-regular graph with \({\rm{100}}\)vertices have?

Short answer

The graph contains \({\rm{2500}}\)edges.

Step-by-step solution

To figure out how many edges there are.

The degree of each vertex is\({\rm{50}}\). As a result, the total number of degrees must be\({\rm{50 \times 100 = 5000}}\).

Result.

As a result of the handshaking theorem, the graph contains \(\frac{{{\rm{5000}}}}{{\rm{2}}}{\rm{ = 2500}}\)edges.