Chartrand–Holbert–Oellermann–Swart conjecture on F-irregular graphs

Let $F$ be a connected graph of order at least $3$. A graph $G$ is $F$-irregular if every vertex of $G$ has a distinct number of subgraphs isomorphic to $F$ that contain it. A graph is nontrivial if it has at least one edge.

Chartrand–Holbert–Oellermann–Swart conjecture. For every connected graph $F$ of order at least $3$, there exists a nontrivial $F$-irregular graph.

The conjecture generalizes the distinction of vertices by ordinary degree, corresponding to $F=K_2$, for which no nontrivial graph is $F$-irregular. It is known for several classes, including stars, complete graphs, and paths, but is not stated as fully resolved here.