so I recently started learning about the graph theory and i came about this question:
Show that a vertex c in the connected simple graph G is a cut vertex if and only if there are vertices u and v, both different from c, such that every path between u and v passes through c.
So from what i understand, a cut vertex is an vertex that if removed, would create 2 graphs from the original. Correct? So to prove the question above, would I simple do:
Is this correct? if not how would I show such case?