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Unformatted text preview: Ex. Recall that we can represent the Königsberg 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. Euler’s 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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This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.
 Spring '08
 EVINSON
 Math, Calculus

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