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Unformatted text preview: Section 50 1. We noticed that a graph with more than two vertices of odd degree cannot have an Eulerian trial, but connected graphs with zero or two vertices of odd degree do have Eulerian trails. The missing case is connected graphs with exactly one vertex of odd degree. What can you say about those graphs ? There aren&t any graphs with exactly one vertex of odd degree. The sum of the degrees of the vertices is equal to twice the number of edges. If there were exactly one vertex of odd degree, the sum of the degrees of the vertices would be an odd number. 2. A domino is a 2 & 1 rectangular piece of wood. On each half of the domino is a number, denoted by dots. In the &gure we show all & 5 2 = 10 dominoes we can make where the numbers on the dominoes are all pairs of values chosend from f 1 ; 2 ; 3 ; 4 ; 5 g ( we do not include dominoes where the two numbers are the same ). Notice that we have arranged the ten dominoes in a ring such that, where two dominoes meet, they show the same number.show the same number....
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This note was uploaded on 07/13/2011 for the course MAD 2104 taught by Professor Staff during the Spring '08 term at FAU.
- Spring '08