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5.7 Eulerizing Graphs

5.7 Eulerizing Graphs. Euler circuit and Euler path do not always exist . There are many graphs (in real life) that have more than 2 odd vertices.

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5.7 Eulerizing Graphs

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  1. 5.7 Eulerizing Graphs

  2. Euler circuit and Euler path do not always exist . • There are many graphs (in real life) that have more than 2 odd vertices. • Instead of finding a route that travels along the edges of a graph and passes through each and every edge of the graph at least once, we want to find a a route that re-cross the fewest number of edges.

  3. Eulerizing of a graph • Eulerizing is the process of changing all odd vertices to even vertices by duplicating appropriate edges

  4. Eulerizing Graphs OPTIMAL ROUTE: duplicate the fewest number of edges First step is to identify the odd vertices. Second step is to add duplicate copies of edges to create all even vertices NOT an optimal route illegal route

  5. Eulerizing the following graphs 1) 2)

  6. Semi-eulerizing of a graph • Semi-eulerizing is the process of leaving 2 odd vertices on the graph unchanged and changing other odd vertices to even vertices.

  7. Semi-eulerizing Graphs OPTIMAL ROUTE:duplicate the fewest number of edges First step is to identify the odd vertices. Second step is leave out 2 oddvertices and add duplicate copies of edges to create even vertices NOT an optimal route illegal route

  8. Semi eulerizing the following graphs 1) 2)

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