Question: Question 6 (20 marks,) Given a graph G, the join of G and Ki is the graph G+ K1 obtained from G by adding a

Question 6 (20 marks,) Given a graph G, the join of

Question 6 (20 marks,) Given a graph G, the join of G and Ki is the graph G+ K1 obtained from G by adding a new vertex (that is, Ki) and joining it to every vertex of G by a new edge. (a) Prove that if G is k-connected, then G Ki is (k+1)-connected (b) Prove that if G is k-edge-connected, then G + Ki is (k +1)-edge-connected

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