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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 19Answer a. 0. b. 2. c. 4. d. 5. e. 1. f. 3.
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 19Answer
a.
0.
b.
2.
c.
4.
d.
5.
e.
1.
f.
3.
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