A clique is a "series" module in the modular decomposition because its
complement is not connected.
See the survey https://arxiv.org/pdf/0912.1457
* A module is of type parallel if G is not connected but its complement it
* A module is of type series if G is connected but its complement is not.
In particular, a clique gives a series module
It is also written in the paper that the smallest prime graph is the P4.
sage: [graphs.PathGraph(i).is_prime() for i in range(5)]
[True, True, False, False, True]
Le lundi 9 juillet 2018 07:47:16 UTC+2, Jori Mäntysalo a écrit :
>
> Graph({1:[2]}).is_prime() returns False, and the documentation says "A
> graph is prime if all its modules are trivial (i.e. empty, all of the
> graph or singletons)".
>
> Is this an error, or are the two-element graphs by convention classified
> as prime graphs?
>
> --
> Jori Mäntysalo
>
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