Exercise 1: Tracing BFS From Vertex 1 — Possible Solution
====================================================================

GIVEN
------------------------------
1 connects to 2, 3
2 connects to 4
3 connects to 5, 6

STEP-BY-STEP BFS TRACE
------------------------------
Start: queue = [1], visited = {1}, order = [1]

Dequeue 1. Neighbors: 2, 3 (both new).
  visited = {1,2,3}, order = [1,2,3], queue = [2,3]

Dequeue 2. Neighbor: 4 (new). (1 already visited)
  visited = {1,2,3,4}, order = [1,2,3,4], queue = [3,4]

Dequeue 3. Neighbors: 5, 6 (both new). (1 already visited)
  visited = {1,2,3,4,5,6}, order = [1,2,3,4,5,6], queue = [4,5,6]

Dequeue 4. No new neighbors (2 already visited).
Dequeue 5. No new neighbors (3 already visited).
Dequeue 6. No new neighbors (3 already visited).

Queue empty - traversal complete.

FINAL BFS ORDER
------------------------------
1, 2, 3, 4, 5, 6

WHY THIS WORKS AS AN ANSWER
------------------------------
The trace follows this chapter's own queue-based, level-by-level BFS
method step by step, processing each vertex's neighbors in the order
given and showing the queue and visited set's own state after each
dequeue, rather than just stating the final order.