For the given multigraph, determine the minimum number of duplicate edges that n

Question

For the given multigraph, determine the minimum number of duplicate edges that need to be added to create an Euler circuit within the new graph. Draw in the new edges. This problem can be used to find the optimal route for snow removal, trash pickup, mail delivery, etc. Note that the edges you add must be duplicates of an existing edge; you cannot connect edges that were not already adjacent. [Hint: Remember what must be true about the vertices to have an Euler circuit. How do you add edges to make that happen?]

Explanation / Answer

For any graph to have an Euler circuit, the necessary condition is that all of its nodes must be even nodes.( i.e. the number of edges at each node must be even. ) We have to add the necessary number of edges in order to fulfill this condition.

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