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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 31ES

Textbook Problem

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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.

To determine

To find if the most efficient way to drive the streets correspond to an Euler circuit, a Hamiltonian circuit, or neither.

**Given information:**

Given, 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.

The officer must return to the starting location when finished.

**Calculation:**

A circuit (that starts and ends at the same vertex) is said to be an Euler circuit if it uses every edge but only once. (i.e...

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