12. For the graph below, find the degree of each vertex. Is there an Euler circuit for this graph? If not explain why not. Find the Hamilton circuit for this graph if there is one. If not, explain why not. B E D

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12. For the graph below, find the degree of each vertex.
Is there an Euler circuit for this graph? If not explain why not.
Find the Hamilton circuit for this graph if there is one. If not, explain why not.
A
E
Transcribed Image Text:12. For the graph below, find the degree of each vertex. Is there an Euler circuit for this graph? If not explain why not. Find the Hamilton circuit for this graph if there is one. If not, explain why not. A E
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Step 1

For the given graph there are 6 vertices, A, B, C, D, E and F.

By definition, degree of of a graph is the number of vertices adjacent to a vertex.

Therefore, the degree of each vertex is,

  • degree of A is 3.
  • degree of B is 2.
  • degree of C is 3.
  • degree of D is 3.
  • degree of E is 2.
  • degree of F is 3.

An Euler circuit is a circuit that uses every edge of a graph exactly once.

Also, if a graph, G has an Euler circuit, then all of its vertices must be even vertices.

From above, only vertices B and E are only even and all the other vertices are even.

Therefore, there is no Euler circuit in the given graph.

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