# Breadth First Traversal for graph with multiple connected components

I read BFS and DFS from CLRS and realized that the BFS algorithm does not consider graph with multiple connected components but only with single connected component, whereas DFS algorithm considers graph with multiple connected components as can be seen in below pic:

Are my observations correct? If yes, why is it like that? Is their any significance to it? Is their any reason for CLRS to give such algorithm or its perfectly acceptable to modify BFS to loop over all vertices, something similar to DFS in order to traverse all connected components of graph?

• for each vertex $$u \in G.V$$:
• if $$u.\text{color} == \textsf{white}$$:
• BFS($$G,u$$)
• Also I was guessing if this will change time complexity of the algorithm. For adjacency list based implementation, it is $O(V+E)$. I believe this will remain unchanged as we check if $u.color==white$. Am I correct? – Rnj Jan 9 '20 at 5:46