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Published byAgnes Singleton Modified over 9 years ago
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5.7 Eulerizing Graphs
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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.
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Eulerizing of a graph Eulerizing is the process of changing all odd vertices to even vertices by duplicating appropriate edges
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Eulerizing Graphs First step is to identify the odd vertices. Second step is to add duplicate copies of edges to create all even vertices OPTIMAL ROUTE: duplicate the fewest number of edges NOT an optimal route illegal route
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Eulerizing the following graphs 1) 2)
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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.
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Semi-eulerizing Graphs First step is to identify the odd vertices. Second step is leave out 2 odd vertices and add duplicate copies of edges to create even vertices OPTIMAL ROUTE:dup licate the fewest number of edges NOT an optimal route illegal route
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Semi eulerizing the following graphs 1) 2)
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