Howard,
It's hard for someone trained as a graph theoristto make sense of that question,
since graphs, strictly speaking, are just dyadic (or binary) relations.
If we are more loosely speaking about the sorts of diagrams that Peirce called
"graphs" and used to represent propositions about arbitrary k-place relations,
then we'll have to take some time to say what those are exactly and what they
represent and how exactly to interpret them.
I might very hazily hazard a guess that are talking about a picture like this:
```````s``
``````/```
o---<R````
``````\```
```````i``
And maybe what you call a "dyadic subgraph" is some 2-part piece of that?
If that is the indeed case, then we'd need to consider very carefully what that
2-part piece of the diagram represents about the intended mathematical object,
which is, we agree, a triadic relation in the strict sense, a set of 3-tuples.
But I'd need to check that guess before going any further down this path.
Regards,
Jon
Howard Pattee wrote:
At 10:04 PM 12/16/2014, Jon Awbrey wrote:
In the best mathematical terms, a triadic relation is a cartesian
product of three sets together with a specified subset of that
cartesian product.
I know that. My question was: Is there a graph theory representation of
a triadic relation that does not have a dyadic subgraph? If so, I was
just looking for a simple example.
Howard
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