Question 1 (3 points) Select all the properties that are true about the graph G above. G is a tree G is directed G is a simple graph G is a forest G is connected G has a non-trivial cycle
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For a graph G ,let L ( G ) denote the so-called line graph of G ,givenby L ( G )=( E, { e, e' } : e, e' ∈ E ( G ) ,e ∩ e' = ∅ ). Decide whether the following is true for every graph G (a) G is connected if and only if L ( G ) is connected. (b) G is Eulerian if and only if L ( G ) has a Hamiltonian cycle ( A Hamiltonian cycle in a graph G is a cycle containing all vertices of G).
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