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The set of automorphisms of a graph form a group under composition because

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The set of automorphisms of a graph form a group under composition because

function composition is associative

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automorphisms are 1:1 and onto

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The composition of two automorphisms is another automorphism

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The composition of two automorphisms is an homomorphism

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there is an identity automorphism

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function composition is always commutative

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1 : 1 and onto functions are exactly those that have inverses

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