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Euler Circuits: The Circuit Comes to...
Quiz #1

1 .       5m1q1_1.gif

Vertex A is adjacent to 



2 .       5m1q1_1.gif

The degree of vertex D is 



3 .       5m1q1_1.gif

The degree of vertex C is 



4 .       5m1q1_1.gif

Which of the following is not a path from vertex D to vertex A? 



5 .       5m1q1_1.gif

Which of the following [A), B), C), or D)] is not a circuit in the graph? 



6 .       5m1q1_1.gif

Which of the following is a bridge of the graph? 



7 .       5m2q7_1.gif

Which of the graphs has an Euler circuit? 



8 .       5m2q7_1.gif

Which of the graphs has an Euler path but no Euler circuit? 



9 .       Questions 9 to 11 refer to the following situation: An undercover police officer is assigned the job of walking once a night each of the 48 blocks of a certain section of town described by the street grid shown below. The walk starts and ends at A. The officer wants to minimize the total number of blocks he has to walk each night.
5m2q9_1.gif

How many vertices of odd degree are there in the graph representing this problem? 



10 .       An optimal eulerization of the graph representing this problem can be obtained by adding 



11 .       Suppose that it takes the officer 5 minutes to walk a block. In an optimal trip, the officer will cover the entire neighborhood in 



12 .       A graph has an Euler circuit if 



13 .       A graph with 11 vertices has an Euler path but no Euler circuit. The graph must have 



14 .       A graph has six vertices—two vertices of degree 4, two vertices of degree 3, and two vertices of degree 2. The number of edges in the graph is 



15 .       The basic rule in Fleury’s algorithm is 



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