- 3. An automorphism of a graph G = (V,E) is any isomorphism of G and...

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- 3. An automorphism of a graph G = (V,E) is any isomorphism of G and G, i.e. any bijection f: V V such that {u, v} = E if and only if {f(u), f(v)} E E. A graph is called asymmetric if its only automor- phism is the identity mapping (each vertex is mapped to itself). (a) Find an example of an asymmetric graph with at least 2 vertices. (b) Show that no asymmetric graph G exists with 1 - 3. An automorphism of a graph G = (V,E) is any isomorphism of G and G, i.e. any bijection f: V V such that {u, v} = E if and only if {f(u), f(v)} E E. A graph is called asymmetric if its only automor- phism is the identity mapping (each vertex is mapped to itself). (a) Find an example of an asymmetric graph with at least 2 vertices. (b) Show that no asymmetric graph G exists with 1