Marco Maggi wrote:
Thanks to all. Am I correct in saying that with a form like:
(a . body)
if the symbol 'a' appears in 'body' the graph is cyclic,
while if the symbol does not appear in its own body the
graph is Acyclic?
Well, it is immediately obvious that any graph (or digraph) which has
such a form has a cycle. So if a graph is acyclic, then no such form
appears. But you also want the converse or its contrapositive: if no
such form appears, then the graph is acyclic; if a graph is cyclic, then
such a form appears.
Are you trying to represent graphs or digraphs?
I. you are representing graphs
The answer is no. (a (b c) c) contains a cycle a-b-c-a, but does not
contain an (a . body) with a in body form.
II. you are representing digraphs
The answer is provisionally no. (a (b c) (c b)) contains a cycle
b->c->b, but no form (a . body) with a in body. However, this graph
could also be represented as (a (b (c b)) c), which does contain such a
form. Notice that in this latter representation, the first time a node
appears, its edge list is given.
So, if we do not require the edge list to be given at the first
appearance of a node, the answer is definitely no. OTOH, if we do make
such a requirement, the answer seems to be yes, but I have not proven
this to be so.
Regards,
Jon
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