1. The graph G is given by the picture 1 2 3 4 5 6 7 8 9 10 11 = (a) Explain why the transposition f = (5,7) (swapping t

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1 The Graph G Is Given By The Picture 1 2 3 4 5 6 7 8 9 10 11 A Explain Why The Transposition F 5 7 Swapping T 1 (112.96 KiB) Viewed 23 times

1. The graph G is given by the picture 1 2 3 4 5 6 7 8 9 10 11 = (a) Explain why the transposition f = (5,7) (swapping the vertices 5 and 7 and leaving all the other vertices fixed) and the product of transpositions g= (1,3)(4,8)(9, 11) define isomorphisms of G with itself. (b) Explain why the graph G is not Hamiltonian. (c) Find all pairs {v, w} of non-adjacent vertices v and w such that the graph G+{v, w} is Hamiltonian. Justify your answer. (Hint: use the symmetries of G given in part (a) to minimise the number of cases to consider.] >