Node A has this relation with node B if every node dominating A also dominates B and neither A nor B dominates the other.

To answer the question step by step:

Step 1: Understand the given relation between Node A and Node B. The relation states that Node A has this relation with Node B if every node dominating A also dominates B, and neither A nor B dominates the other.

Step 2: Identify the concept of domination in this context. Domination refers to the relationship between nodes in a graph, where one node dominates another if it is reachable from the dominating node by following directed edges.

Step 3: Consider the first part of the relation, which states that every node dominating A also dominates B. This means that if there is a node X that dominates A, it must also dominate B. In other words, any path from A to X must also include B.

Step 4: Consider the second part of the relation, which states that neither A nor B dominates the other. This means that there is no direct path from A to B or from B to A. In other words, A and B are not directly connected in terms of domination.

Step 5: Combine both parts of the relation to understand the overall relationship between A and B. Based on the given conditions, A and B are related in such a way that any node dominating A must also dominate B, but there is no direct domination relationship between A and B.

Step 6: Summarize the relation between Node A and Node B. In conclusion, Node A has this relation with Node B if every node dominating A also dominates B, and neither A nor B dominates the other.