Choosing edge in Kruskal's algorithm to form MST

Question

In the given picture, I was trying to form an Minimum Spanning Tree and I wonder if we can select the edge (FB) because it crosses an another edge (AG).

Thanks in advance.

Answer 1

Crossing in a graph the way you probably mean it depends on the particular embedding of the graph on the plane, so it does not mean much for the actual graph when you are trying to find a minimum spanning tree. (A graph can have infinitely many ways of embedding it on a plane)

The way Kruskal's algorithm works is that at every step you choose an edge $uv$ such that $u$ and $v$ are in different components, and $uv$ is the lightest edge satisfying this property.