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4. An automorphism of a graph is an isomorphism of the graph onto itself. (a) Show that an automorphism of a simple graph G can

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4. An automorphism of a graph is an isomorphism of the graph onto itself. (a) Show that an automorphism of a simple graph G can be regarded as a permutation on V which preserves adjacenty, and that the set of such permutations form a group I(G) (the automorphism group of G) under the usual operation of composition. (b) Find I(K) and I(Km,n) (c) Find a nontrivial simple graph whose automorphism group is the identity

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