Question

a security guard needs to walk the streets of the neighborhood shown to the right, walking each street once. complete parts (a) and (b) below.
b. determine whether the residents in the neighborhood will be able to establish a route for the security guard so that each street is walked exactly once. if this is possible, use your map to show where the guard should begin the walk. choose the correct answer below
a. no, there is no route
b. yes, there is a route. the guard can start at vertex c or vertex f.
c. yes, there is a route. the guard can start at any vertex.

Explanation:

Step1: Recall Euler's path theorem

An Euler path exists in a graph if and only if the graph has exactly 0 or 2 vertices of odd degree.

Step2: Analyze the degrees of vertices in the graph

Count the number of edges connected to each vertex (degree of the vertex). After counting, we find that there are exactly 2 vertices with odd degrees.

Step3: Determine the start and end vertices

According to Euler's path theorem, if there are 2 vertices of odd degree, the Euler path starts at one of the odd - degree vertices and ends at the other.

Answer:

B. Yes, there is a route. The guard can start at vertex C or vertex F.