Consider the pseudocode for breadth$-$first search in $($a$.)$ above.

Define the distance between two vertices x and y in a graph as being the minimal number

of edges between them. The distance from a vertex to itself is $0$; if the graph is not

connected, and there is no path between the vertices x and y$,$ the distance is $\backslash$infty $.$

In the graph in $($a$.),$ the following are some example distances.