I have recently started studying graphs and their different traversal algorithms, and can't seem to be able to come up with answers to these two questions. I really need your help, I don't even know where to start.
(a) Prove that every connected graph G=(V,E) has a node v∈V such that removing vv and all its adjacent edges will not disconnect G.
(b) For a given connected graph G=(V,E), design an O(n+m)-time algorithm to find such a node.
I have found some answers here, but they still don't make a lot of sense to me because I don't have a lot of experience in the topic.
Thank you so much in advance!