#12626: Kautz, Imase and Itoh, and Generalized de Bruijn digraph generators
----------------------------+-----------------------------------------------
Reporter: dcoudert | Owner: jason, ncohen, rlm
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-5.0
Component: graph theory | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: David Coudert
Merged: | Dependencies:
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Comment(by ncohen):
Helloooo David !!!
Well, I only have two unimportant things to bring up, and a question :
* Your "TESTS ::" should become "TESTS :" on two occurrences. There
should only be a "::" before some Sage code, not before text !
* An integer equals to the diameter --> equal
I also spent some time playing with the code of the Kautz constructor. I
have to admit I am not a big fan of doing all the computations through
words, if you end up casting them to strings in the end. I don't think it
would be a good idea to keep words in the graph either, as then the
vertices would appear as "word: 1" instead of '1', hence it is not a good
idea either. If you only need the is_suffix method you can just use string
methods :
{{{
sage: a = "123456789"
sage: a[1:]
'23456789'
}}}
This would mean that all of your symbols have a 'width' of 1, though.
Hence, "Bb" could not be a symbol as in your examples.
The other thing is that as such, it is not possible to "decompose" a
vertex of your graph. Vertices are strings of symbols split by commas, but
you have no idea what the "first symbol of the word" is. The answer to
that would be to use tuples ("Bb", '1') to encode the vertices, but of
course they would be longer.
All this to say that I do not know of any "good solution" to the problem.
I'm just bringing this up for you to decide, after all you know better
than I do what these graphs can be used for `:-)`
Oh, and.. I would have changed
{{{
produced, and also to the cardinality minus one of the alphabet to use.
}}}
by
{{{
produced, that is the cardinality [...]
}}}
to make clearer that it is an equivalent definition. That again is up to
you !
Nathann
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12626#comment:5>
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