# Largest Number of Edges

**Discrete Mathematics**Level 5

Suppose \(G\) is a connected, simple, planar graph with \(100\) vertices. What is the largest possible number of edges in \(G\)?

**Details and assumptions**

A graph is **connected** if there is a path from any one vertex to any other.

A graph is **simple** if it contains no loops and no multiple edges.

A **loop** is an edge whose endpoints coincide.

A **multiple edge** is an edge whose endpoints are identical to the endpoints of another edge.

A graph is **planar** if it can be drawn so that no two edges intersect at points other than their endpoints. The edges need not be straight line segments, and can be curved lines.