3. Given a directed acyclic graph G = (V, E) and two vertices s, t EV, design an efficient algorithm that computes the number of different directed paths from s to t.

Computer Networking: A Top-Down Approach (7th Edition)
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3.
4.
Given a directed acyclic graph G = (V, E) and two vertices s, te V, design an efficient
algorithm that computes the number of different directed paths from s to t.
Define the incidence matrix B of a directed graph with no self-loop to be an nxm matrix
with rows indexed by vertices, column indexed by edges such that
Bij
=
-1
1
0
if edge j leaves vertex i,
if edge jenters vertex i,
otherwise.
Let BT be the transpose of matrix B. Find out what the entries of the n x n matrix BBT stand for.
Transcribed Image Text:3. 4. Given a directed acyclic graph G = (V, E) and two vertices s, te V, design an efficient algorithm that computes the number of different directed paths from s to t. Define the incidence matrix B of a directed graph with no self-loop to be an nxm matrix with rows indexed by vertices, column indexed by edges such that Bij = -1 1 0 if edge j leaves vertex i, if edge jenters vertex i, otherwise. Let BT be the transpose of matrix B. Find out what the entries of the n x n matrix BBT stand for.
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