Hi, at ua-cam.com/video/ahxThTOi8Jw/v-deo.html you are drawing the edge from Vo to Vi, hence we are able to prove the cycle and contradict the statement, but if the edge is from Vo to some other Vertex Vj, which is not in the longest path, then how to prove drawing edge between Vo-Vj creates a cycle?
Thanks for watching and that depends, because our result that tree graphs have at least two end vertices relies on definitions specifically for undirected graphs. So you'd have to specify the definitions you want to use to consider the result for directed graphs. For example, does a "directed tree" have to be strongly connected (a path connecting every pair of vertices in both directions) or only weakly connected (the underlying undirected graph is connected)?
could we say that smallest possible non trivial tree contains 2 vertices, since it has only two connected vertices, it has 2 end V. And all other trees are 2 or more so all tree graphs have at least 2 end V. I am not so good at math, excuse me if I sound foolish.
![[Discrete Mathematics] Vertex Degree and Regular Graphs](http://i.ytimg.com/vi/k7ThfZIT_ac/mqdefault.jpg)
Your videos are saving my semester in university! Thank you so much
How'd the rest of your semester go?
Appreciate the early heads-up on usage of this proof. I was about to skip this proof deeming not useful :)
Two end vertices? More like "Terrific videos that are must see!"
Can you do videos on probabilistic proofs of graphs?
Sir can you say about coedge split dominating set with examples
Hi, at ua-cam.com/video/ahxThTOi8Jw/v-deo.html you are drawing the edge from Vo to Vi, hence we are able to prove the cycle and contradict the statement, but if the edge is from Vo to some other Vertex Vj, which is not in the longest path, then how to prove drawing edge between Vo-Vj creates a cycle?
What if the edges are directed, then v_0 -> v_1 would not form a cycle.
Thanks for watching and that depends, because our result that tree graphs have at least two end vertices relies on definitions specifically for undirected graphs. So you'd have to specify the definitions you want to use to consider the result for directed graphs. For example, does a "directed tree" have to be strongly connected (a path connecting every pair of vertices in both directions) or only weakly connected (the underlying undirected graph is connected)?
could we say that smallest possible non trivial tree contains 2 vertices, since it has only two connected vertices, it has 2 end V. And all other trees are 2 or more so all tree graphs have at least 2 end V. I am not so good at math, excuse me if I sound foolish.