Question: Eular Path Name: Euler Paths and Circuits Worksheet 1. In the graph below, the vertices represent houses and two vertices are joined by an edge

Eular Path

Name: Euler Paths and Circuits Worksheet 1. In the graph below, the vertices represent houses and two vertices are joined by an edge if it is possible to drive between the two houses in under 10 minutes. a. How many vertices does the graph have? b. How many edges does the graph have? c. What is the degree of A? d. What is the degree of E? e. Is it possible to drive from house A to house G in less than 20 minutes? Explain. 2. Draw a connected graph with vertices A, B, C, and D in which the degree of vertices A and D is 3 and the degree of vertices B and C is 2. 3. Draw a connected graph with eight vertices where each vertex has degree 3. 12 UNIT 1 4. Consider the path represented by the sequence of numbered edges on the graph below. Explain why the given path is not an Euler circuit. b. 2 3

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