For n Z+ where n 4, let V' = {v1 v2, v3, . . .

Question:

For n ∈ Z+ where n ≥ 4, let V' = {v1 v2, v3, . . . , vn-1} be the vertex set for the complete graph Kn-1Construct the loop-free undirected graph Hn = (V, E) from Kn-1 as follows:
V = V' ∪ {u}, and E consists of all the edges in Kn-1 together with the new edge {v, v1}.
(a) Show that Hn has a Hamilton path but no Hamilton cycle.
(b) How large is the edge set E?