ALGORITHM $BFS(G)$

$//$Implements a breadth$-$first search traversal of a given graph

$//$Input: Graph $G=($:$V,E$:$)$

$//$Output: Graph $G$ with its vertices marked with consccutive integers

$//$in the order they have been visited by the BFS traversal

mark each vertex in $V$ with $0$ as a mark of being "unvisited"

count larr$0$

for each vertex $v$ in $V$ do

if $v$ is marked with $0$

$\frac{b}{s}(v)$

$bfs(v)$

$//$visits all the unvisited vertices connected to vertex $v$ by a path

$//$and assigns them the numhers in the order they are visited

$//$via global variable count

count larr count $+1$ ; mark $v$ with count and initialize a queue with $v$

while the queue is not empty do

for each vertex $w$ in $V$ adjacent to the front vertex do

if $w$ is marked with $0$

count larr count $+1$;$,$ mark $w$ with count

add $w$ to the queue

remove the front vertex from the queue