Some confusion about time-complexity and A*.
According to A* Wiki the time-complexity is exponential in the depth of the solution (shortest path):
The time complexity of A* depends on the heuristic. In the worst case of an unbounded search space, the number of nodes expanded is exponential in the depth of the solution (the shortest path) d: $O(b^d)$, where $b$ is the branching factor (the average number of successors per state).
The comment to this accepted answer points out that it makes more sense to give the complexity in termes of the size of the graph and therefore it should be $O((|V| + |E|) \cdot log |V|)$
Obviously, if the heuristic assigns a value of 0 to every node, A* becomes Dijkstra's algorithm and any uniform cost heuristic will essentially disable the heuristic.
If we assume the heuristic to be $O(1)$ (and consistent), it would make sense that the worst case is essentially degrading A* to Dijkstra's algorithm which has complexity
with a min-priority queue implementation (Fibonacci heap).
Am I wrong?
Any book etc I have been looking at always gives the complexity in terms of the depth of the solution