Determining complement graphs

Reference no: EM13123403

(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. (Please read carefully the definition of an induced subgraph before you attempt to solve it!).

Simple graph is a graph with no loops or multiple edges. K_1 is also a tree.

(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?

(3) Prove or disprove: Every graph with fewer edges than vertices contains a component that is a tree.

Reference no: EM13123403

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