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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 DFSG
and DFSGT
have no forwardedges and no crossedges.
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 nonselfloop edge from G
will make it not strongly connected.
G
is monopathic if and only if DFSG
has no forwardedges and no crossedges, and for each vertex u
other than the DFSroot, there is a unique backedge xy
such that x
is a descendant of u
and y
is a proper ancestor of u
with respect to the DFStree
Question Answer
a
b
c
d
e
f
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