Discussion:
Q(1) Let G be a simple graph with no isolated vertex and no induced subgraph with exactly two edges. Prove that G is a complete graph.
Simple graph is a graph with no loops or multiple edges. K_1 is also a tree.
Q(2) Let v be a cut-vertex of a simple graph G. Prove that complement(G) - v is connected. (The graph we are talking about is the complement of G with v removed.)
(By "complement (G)-v" mean "find the complement if G and remove v from it"
However, if you do it the other way , remove vfrom G and them find a complement of it (denoted then by complement (G-v),don't you get the graph?
Q(3) Prove or disprove: Every graph with fewer edges than vertices contains a component that is a tree