Answer
This graph has four odd vertices, so according to Euler's theorem, there are no Euler paths for this graph. Therefore, it is not possible to establish a route for the security guard so that each street is walked exactly once.
Work Step by Step
An Euler path is a path that travels through every edge of a graph exactly once. We need to determine if this graph has an Euler path.
According to Euler's theorem, for a graph to have at least one Euler path, the number of odd vertices must be either 0 or 2. On this graph, vertex B, vertex D, vertex F, and vertex H are odd vertices. This graph has four odd vertices.
Therefore, according to Euler's theorem, there are no Euler paths for this graph. Therefore, it is not possible to establish a route for the security guard so that each street is walked exactly once.
