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Asked May 14, 2019
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16. Does this graph have an Eulerian circuit? If not, why not? If so, list one.
List a Hamiltonian circuit for this graph
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16. Does this graph have an Eulerian circuit? If not, why not? If so, list one. List a Hamiltonian circuit for this graph

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Expert Answer

Step 1

The given graph is shown in the below figure.

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Step 2

Interpretation:

A graph is said to be Eulerian graph if it is a connected graph and every vertex of the graph has even degree.

Here, the degree of the vertex A, B, C, D, E, F and G are 2, 4, 4, 4, 4 and 2.

Since the graph is connected with all the vertices have even degree, the graph is an Eulerian.

Thus, Eulerian Circuit exits for the given graph.

Eulerian path is a path in graph that visits every edge exactly once. Eulerian Circuit is an Eulerian Path which starts and ends on the same vertex.

The Eulerian Circuit for the given graph is A-B-C-D-B-E-F-D-E-G-F-C-A.

Step 3

A Hamiltonian path is a path in a graph which visits each vertex exactly once. A Hamiltonian circuit is a cycle which visits each vertex exactly once and also returns to ...

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