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Unformatted text preview: Ex. Recall that we can represent the Knigsberg bridge problem using the graph below. Ex. Ex. If we carefully read through the two theorems described earlier, we see that they do not consider the case where exactly one odd vertex appears in a graph. The following theorem explains that this situation is impossible. Eulers Sum of Degrees Theorem i) The sum of the degrees of all the vertices of a graph equals twice the number of edges (and is hence even). ii) A graph always has an even number of odd vertices. So to summarize, if you calculate the number of odd vertices, then the following conclusions can be reached. Number of Odd Vertices Conclusion...
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 Spring '08
 EVINSON
 Math, Calculus

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