I understand that, in tree search, an admissible heuristic implies that $A*$ is optimal. The intuitive way I think about this is as follows:
Let $P$ and $Q$ be two costs from any respective nodes $p$ and $q$ to the goal. Assume $P<Q$. Let $P'$ be an estimation of $P$. $P'\le P \Rightarrow P'<Q$. It follows from uniform-cost-search that the path through $p$ must be explored.
What I don't understand, is why the idea of an admissible heuristic does not apply as well to "graph-search". If a heuristic is admissible but inconsistent, would that imply that $A*$ is not optimal? Could you please provide an example of an admissible heuristic that results in a non-optimal solution?