Final answer:
In a BFS tree, a dashed edge cannot connect vertices that are three levels apart because in BFS, exploration happens level by level, with each BFS tree level corresponding to a set distance from the root. A dashed edge connects only adjacent nodes in a BFS tree.
Step-by-step explanation:
Is it possible for a dashed edge to connect vertices on a BFS tree that are 3 layers/levels apart? The answer is No.
In Breadth-First Search (BFS), the algorithm explores the graph level by level, starting from the root node and working its way through neighboring vertices one layer at a time. A BFS tree is therefore a representation of this process, where each level of the tree corresponds to nodes that are the same distance from the root. A dashed edge typically represents an explored edge that does not belong to the resulting BFS tree. Since neighboring nodes in a BFS are adjacent, a dashed edge cannot connect vertices three layers apart, as it would conflict with the level-by-level exploration rule of BFS.