Consider the graphs $G=(V,E)$ where there exists a non-empty $S \subseteq V$ such that $G[S]$ is a complete subgraph and every possible edge between $S$ and $V\setminus S$ is present in $G$. Equivalently, every vertex in $S$ is "universal", that is, is a neighbor of every other vertex in the graph.

I found this class of graphs during my research and I don't know if there is a name for them. Any reference would be appreciated.


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