Let G = (V, E) be a simple undirected graph, and s be a particular vertex in it called the source. For x ∈ V, let d(x) denote the shortest distance in G from s to x. A breadth first search (BFS) is performed starting at s. Let T be the resultant BFS tree. If (u, v) is an edge of G that is not in T, then which one of the following CANNOT be the value of d(u) – d(v)?
(A) -1
(B) 0
(C) 1
(D) 2


Answer: (D)

Explanation: Note that the given graph is undirected, so an edge (u, v) also means (v, u) is also an edge.

Since a shorter path can always be obtained by using edge (u, v) or (v, u), the difference between d(u) and d(v) can not be more than 1.

Quiz of this Question