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) For an n-vertex graph G (with n 1), the following are equivalent (and characterize the trees with n vertices) I) G is connected and has no cycles

) For an n-vertex graph G (with n ≥ 1), the following are equivalent (and characterize the trees with n vertices)


I) G is connected and has no cycles

II) G is connected and has n-1 edges

III) G has n-1 edges and no cycles

IV) G has no loops and has, for each u, v ∈ V(G), more than one u, v-path

Which one is true ?

I and II are true

I, II and III are true

Only IV is true

All are true

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