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user 8193
Questions of the kind "What's the name for a X that satisfies property Y?"
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Accepted
Is there a standard term for this graph/set theoretic concept?
You can think in terms of intersection graphs. The transitive adjacency tells you when two vertices are adjacent. The adjacency union is then empty if and only if two of $E_1,\ldots,E_k$ are in distin …
1
vote
Have this subclass of split graphs been studied before?
I don't know if this can help you, but it's easy to see that your class is a superclass of connected threshold graphs. I think that the inclusion is strict, since $S_3$(link) is in your class, but is …