Graph theory basics

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   A simple graph on $n = 8$ vertices has $e = 17$ edges. How many edges does its complement have (the graph on the same vertex set containing exactly the pairs of vertices that are NOT edges of the original)?

2. Warm-up

   A simple graph on $n = 6$ vertices has $e = 2$ edges. How many edges does its complement have (the graph on the same vertex set containing exactly the pairs of vertices that are NOT edges of the original)?

3. Warm-up

   A simple graph on $n = 12$ vertices has $e = 34$ edges. How many edges does its complement have (the graph on the same vertex set containing exactly the pairs of vertices that are NOT edges of the original)?

Problems shown under their original terms: Generated (template, solver-computed).