- Background information: I am studying graph theory in discrete mathematics. I have come across this question, but my solution contradicts my professor solution, and I don't understand some parts of the provided solution. I need help with reasoning and understanding her answer.
- Original question and professor solution:
- My solution:
I think the answer is true because considering a (u,v) path of {(u,x), (x,w), (w,x), (x,v)} , we can easily see that (x,w) and (w,x) exist which prove that (u,v) path passes through w, and contains w.
- My question:
Why does my professor say that the (u,v) path in G does not contain vertex w? And will the (u,v) path pass through vertex w?
A path cannot repeat vertices. In the "path" you've written, x is visited twice.
[Edit]
Here is a reference for the path, trail, walk, cycle, and circuit definitions.
What is difference between cycle, path and circuit in Graph Theory