What're pairwise, vertex disjoint copies of $K_5$?

Question

I need some help nailing some graph theory terminologies down. I know that a planar graph $G$, is a graph where no two edges intersect one another. A vertex disjoint graph $G1$ is a graph, where $V(G1_1) \ \cap V(G1_2)=\emptyset$, or each sub graph of $G1$ don't share any edges. $K_5$ is a non-planar graph which has $5$ vertices which're connected to one another by edges. However I'm unsure as to what pairwise, vertex disjoint copies of $K_5$ are. It would be great if someone can explain in intuitive English what that is.

Answer 1

Here is one $K_5$: a graph with $5$ vertices (which I've numbered $1$ to $5$), with an edge connecting each pair of vertices.

Here are two vertex-disjoint copies of $K_5$. Ten vertices ($1$ to $10$). The first five form one copy of $K_5$, since each pair of them is connected by an edge. The second five form the other copy of $K_5$, again each pair connected by an edge. They are vertex-disjoint since no vertex in the first five is in the second five.

BTW: your statement about a planar graph is faulty. A planar graph is one that can be drawn so that no two edges cross each other. This is a planar graph, even though there are crossing edges in the picture:

because you can draw it so those edges don't cross: