I was studying about subgraph and I have question about it.
So let's say there is a graph G which has two nodes, A and B, and an edge connecting node A and B. I learned that graph can be called by nodes. So this graph G can be also called as graph AB.
Then there is a subgraph of G which also has two nodes, A and B, but no edge connecting node A and B. In this case, is it also called as graph AB? or is there any other way to call it? I am confused.
Thank you for the answer
On
No, graphs are usually not called AB or CD or DFG.
As you noticed such a notation would be ambiguous.
Usually one writes a graph as $G=(V,E)$,
where $V$ is the set of vertices and
$E$ is the set of edges of the graph.
I would denote the main graph as:
$G_1 = (\{A,B\}, \{AB\})$
and the subgraph as
$G_2 = (\{A,B\}, \emptyset)$
Usually the graph with two nodes connected by an edge is called $K_2$, the complete graph on two vertices.
In your case, you have the complement of this, so I would write $\overline K_2$.