# Special type of "Bipartite" graph

How do you call a graph that the bipartite property is satisfied for the one set of nodes and not the other?

Say you have two set of nodes $$A$$ and $$B$$ where there can be edges between nodes of set $$A$$ but there can be no edges between nodes of set $$B$$.Of course there can be edges between nodes of different sets.Is there a name for this type of graph?

• No, there is no special name, and indeed you can do this for any graph (just take any independent set of vertices to form $B$ and the rest of the vertices form $A$). Dec 7 '20 at 11:28
• That could be any graph, right? Let $G$ be any graph, let $B$ be any independent set of nodes (no edges between them) in $G$, and let $A$ be the rest of the nodes in $G$.
– bof
Dec 7 '20 at 11:29
• You could say that this holds iff $A$ is a vertex cover of the entire graph if that helps. Dec 7 '20 at 19:20

This is more a characteristic of $$B$$. A subset $$B$$ of the nodes of a graph that have no edges between each other is called an independent set.
Every independent subset fulfills the criterion of the question, and every $$B$$ that fulfills the criterion of the question is inversely an independent subset.
Note that there are actually no criteria on $$A$$ other that it's the remaining graph, after removing $$B$$.