Find a graph for which Kruskal's algorithm achieves worst-case running time
Let the answer be a complete graph $G = (V,E)$ with $|V| = n$ and a weight function $W : E \to \mathbb{R}$

Let the vertices be denoted by $1,2,\dots n$ and edges between $i$ and $j$ as $(i,j)$.

Now define the weights of all the edges as follows:
$$W(i,j) = j-1, \forall \ 1 \le i &lt; j$$

(Assuming you break ties for the edges on the basis of the value of the nodes $i,j$)

If you add a break statement once all $n$ nodes have been merged, then the algorithm will iterate on all the $\binom{n}{2}$ edges (except the last $n-1$) before finishing execution. This is because it will iterate all the edges in non decreasing order and it will find that except for the edge $(1,j)$ all other edges connect nodes belonging to the same disjoint set.

The running time will thus be $\mathcal{O}(\alpha(n + \binom{n}{2}))$