Estimating the exact runtime of the A* algorithm on an unexplored graph can be challenging because it depends on the specific characteristics of the graph, such as the branching factor and the depth or distance from the start node to the goal node. However, it is possible to provide an upper bound on the worst-case runtime based on these factors.

To estimate the worst-case runtime, you need to consider the branching factor (b) and the depth or distance (d) in the graph. The branching factor represents the average number of successors or neighbors that each node has. In the worst case, the A* algorithm would need to explore all possible nodes up to a certain depth or distance to find the goal node.

The worst-case runtime complexity of the A* algorithm is typically expressed as O(b^d). This means that the runtime grows exponentially with respect to the branching factor and the depth of the graph. If the branching factor is high and the depth is large, the algorithm's runtime can increase significantly.

The branching factor (b) can be calculated or estimated based on the specific problem or graph. For example, in a grid-based graph where each node has four or eight neighbors (up, down, left, right or including diagonals), the branching factor would be 4 or 8, respectively. In other cases, it may require domain-specific knowledge or analysis to estimate the branching factor accurately.

Regarding the graph type, the A* algorithm can work on both directed and undirected graphs. The directionality of the graph does not affect the algorithm's basic principles. However, for directed graphs, it is important to ensure that the heuristic function used in A* is consistent or admissible to guarantee the optimality of the solution.
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