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A digraph G is said to be monopathic if for every pair of its distinct vertices u and v there is at most one simple

A digraph G
is said to be monopathic if for every pair of its distinct vertices u
and v
there is at most one simple path directed from u
to v
(and at most one from v
to u
).
Now let G
be an arbitrary strongly connected digraph. How many of the following five statements are true?
G
is monopathic if and only if GT
is monopathic.
G
is monopathic if and only if both DFS(G)
and DFS(GT)
have no forward-edges and no cross-edges.
G
is monopathic if and only if any pair of distinct simple cycles in G
have at most one vertex in common.
G
is monopathic if and only if removal of any single non-self-loop edge from G
will make it not strongly connected.
G
is monopathic if and only if DFS(G)
has no forward-edges and no cross-edges, and for each vertex u
other than the DFS-root, there is a unique back-edge (x,y)
such that x
is a descendant of u
and y
is a proper ancestor of u
(with respect to the DFS-tree).
Question 24Answer
a.
2.
b.
5.
c.
0.
d.
3.
e.
1.
f.
4.

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