A tree is a circuit-free connected graph. A leaf is a vertex ofdegree 1 in a tree. Show that every tree T = (V, E) has thefollowing properties: (a) There is a unique path between every pairof vertices. (b) Adding any edge creates a cycle. (c) Removing anyedge disconnects the graph. (d) Every tree with at least twovertices has at least two leaves. (e) | V |=| E | +1.
