Question 2.87

57. For each of the accompanying diagrams, explain why the wiggly edges are not

  1. a spanning tree.
  2. a Hamiltonian circuit.
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75

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57.

Diagram (a): (a) There is a circuit and wiggled edges do not include all vertices. (b) The circuit does not include all the vertices of the graph.

Diagram (b): (a) The tree does not include all vertices of the graph. (b) Not a circuit

Diagram (c): (a) Not a tree (b) Not a circuit

Diagram (d): (a) Not a tree (b) Not a circuit