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3. Provide a graph (aside from the examples in our class discussion) that has an Eulerian path. Trace the Eulerian path through the labelled vertices.

3. Provide a graph (aside from the examples in our class discussion) that has an Eulerian path. Trace the Eulerian path through the labelled vertices.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.5: The Format Proof Of A Theorem
Problem 12E: Based upon the hypothesis of a theorem, do the drawings of different students have to be identical...
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Aside from the example given in the next picture.thank you

3. Provide a graph (aside from the examples in our class discussion) that has an Eulerian path. Trace the Eulerian path through the labelled vertices.
Transcribed Image Text:3. Provide a graph (aside from the examples in our class discussion) that has an Eulerian path. Trace the Eulerian path through the labelled vertices.
b. Using the Eulerian Graph Theorem, this graph is not Thus, it is not possible for the biker to traverse all the Example 4: An Application of Euler Path Theorem Below is the map of all the trails in a A biker would like to traverse all the trails exactly on a. Is it possible for the biker to plan traverses all the trails exactly once? Mathematics in the Modern World 5.3 На a trip that and return to the starting point without repeating nd trail in the trip? any Sir Willia C In once, į contrar exactly edges. Graph Euler Solution: determ graph. a. By the Euler Path Theorem, the map shows an Euler path since the graph has two vertices of odd degree with all other vertices of even degree. By trial and error, the path A - B - E - F - D-B - C - F –G – C – A – G uses every edge without duplication, hence an Euler path. Thus, it is possible for the biker to plan a trip that traverses all the trails exactly once. The trip starts at point A, a vertex with an odd degree and ends at point G, the other vertex with an odd degree. b. Using the Eulerian Graph Theorem, this graph is ho Eulerian since vertices A and G both have odd degrees. Dira verti verti leas Exam wheth trails and return to the starting point without repeatno any trail in the trip. right or no Hamil is not 102 F.
Transcribed Image Text:b. Using the Eulerian Graph Theorem, this graph is not Thus, it is not possible for the biker to traverse all the Example 4: An Application of Euler Path Theorem Below is the map of all the trails in a A biker would like to traverse all the trails exactly on a. Is it possible for the biker to plan traverses all the trails exactly once? Mathematics in the Modern World 5.3 На a trip that and return to the starting point without repeating nd trail in the trip? any Sir Willia C In once, į contrar exactly edges. Graph Euler Solution: determ graph. a. By the Euler Path Theorem, the map shows an Euler path since the graph has two vertices of odd degree with all other vertices of even degree. By trial and error, the path A - B - E - F - D-B - C - F –G – C – A – G uses every edge without duplication, hence an Euler path. Thus, it is possible for the biker to plan a trip that traverses all the trails exactly once. The trip starts at point A, a vertex with an odd degree and ends at point G, the other vertex with an odd degree. b. Using the Eulerian Graph Theorem, this graph is ho Eulerian since vertices A and G both have odd degrees. Dira verti verti leas Exam wheth trails and return to the starting point without repeatno any trail in the trip. right or no Hamil is not 102 F.
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