I've been studying graph theory recently and I find it very interesting. But since I'm studying it on my own, I feel like I'm missing something - for example, I'm struggling with these two problems:
- If for whichever two vertices a and b in the graph G there is only one simple path from a to b, then the graph is a tree.
Eh... isn't this part of the definition for a tree? I really don't even know where to start with proving this statements. I would really like to see a good proof laid out, so if anyone can help, please do! :)
Another one: 2. Find which complete bipartite graphs are complete.
What does it mean which COMPLETE bipartite graphs are complete? Can a complete bipartite graph not be complete? I would also love to see a good solution to this. It's really interesting and it bother's me that I can't solve it.
Any help is very much appreciated!