Terms of graph theory in english

Question

Can anyone please tell me how are these graphs called in english?

1. If we can divide a set of graph vertices in two disjoint sub sets, such as all edges connect vertices only inside these sub sets? How are those graphs called?

2. The property of graph is called......, if for every graph G we can say that this graph has this property if subgraph G - v, v in G(V) has this property.

I just need to these words in english, so i can google them. There is very little material on those things in language I study in.

Answer 1

I'm not sure if these are what you are looking for, but seem relevant:

• a connected graph, connectivity,
• a bipartite graph, bipartiteness,
• a hereditary property, hereditariness.

I hope this helps $\ddot\smile$

Answer 2

If the vertex set of a graph can be partitioned into two subsets $V=V_1 \cup V_2$ such that no edge is from a vertex in $V_1$ to a vertex in $V_2$, then the graph is said to be disconnected. The graph then has at least two connected components, and it has exactly two connected components if the two induced subgraphs $G[V_1]$ and $G[V_2]$ are connected.

A hereditary property is a property of a graph that holds for all induced subgraphs of $G$, whereas you are looking for a property that holds only for certain kinds of induced subgraphs of $G$, namely all the vertex-deleted subgraphs $G-v$. I don't know off-hand if there is a name for such a property.