Prove that at least as many edges as vertices implies a cycle I am EXTREMELY confused on where to start with this problem. We recently just started learning about graph theory and I don't know where to begin.


  Prove that in a connected graph G with $p$ vertices, $q$ edges, and at least one cycle, $q \ge p$


How do I begin with this question? Any help would be greatly appreciated. Thank you so much.
Graph has a cycle on $k$ vertices implies that those vertices are connected with $k$ edges. Also, the graph is connected so $p-k$ vertices which left should be connected to the cycle, that means extra $p-k$ edges (distinct end points). Totally the graph has more($\geq$) than $p$ edges.