#15060: The empty graph once again
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Reporter: darij | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: graphs, border cases, bitset, | Merged in:
memleak | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by kcrisman):
As a non graph-theorist... I was wondering whether the empty graph should
be a connected graph with zero connected components. Though one of the
definitions on that math.SX question suggested one connected component is
the definition of connected.
So... what do the various standard texts say about this? Maybe they are
silent on the question?
Note that apparently there is still enough disagreement about the
definition that the Wikipedia article on the related set question
(connectedness) points it out, though without references.
Perhaps it is better to *document* that we follow a certain convention
(probably the more obvious one, in this case), and then in documentation
for anything about connected components point it out again. If we really
have to. I don't quite see why there are infinitely many decompositions,
since the empty graph does not have any connected components (which is not
quite the same as a connected graph) - or perhaps I err in thinking a
component has to be non-empty. Naturally, this is all just deciding on a
definition. But it's not quite the same as 1 not being a prime number
(and note Conway's argument that 1 and -1 ''do'' count, but as prime
''powers'', not "primes", whatever those are - perhaps something analogous
could work with sets or graphs, who knows).
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Ticket URL: <http://trac.sagemath.org/ticket/15060#comment:9>
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