Graphs & greedy algorithms

What is the best possible (or most tight) big O notion of the time complexity of the breadth first search algorithm in the worst case? Give a brief reason. Hint. The challenge is we don't know how many times the while loop is repeated. However, we do know that for any node of the graph, it can occur at most once in Line 4 of the algorithm, which means that the line 4 will be repeated at most n times where n is the number of the nodes of the graph. Hence, the body of the while loop is repeated at most n times. Another challenge is the for loop in line 9. There are at least two options: an easy one is to assume it is repeated at most n times, and a more challenging one is n, time which is the number of neighbors of node u. For the latter options, you may use the result that the sum of the n, for all node u of a graph is two times the number of the edges of the graph