Chapter 5.2, Problem 31ES

Route Planning A security officer patrolling a city neighborhood needs to drive every street each night. The officer has drawn a graph to represent the neighborhood in which the edges represent the streets and the vertices correspond to street intersections. Would the most efficient way to drive the streets correspond to an Euler circuit, a Hamiltonian circuit, or neither? (The officer must return to the starting location when finished.) Explain your answer.