A graph $G$ with $n$ vertex is called good if every vertex could be labelled with distinct positive integers which are less than or equal $\lfloor \frac{n^2}{4} \rfloor$ such that there exists a set of nonnegative integers $D$ with the following property: there exists an edge between $2$ vertices if and only if the difference of their labels is in $D$. Show that there exists a positive integer $N$ such that for every $n \ge N$, there exist a not-good graph with $n$ vertices.
Problem
Source: 2011 Indonesia TST stage 2 test 5 p2
Tags: floor function, graph, graph theory, combinatorics