   # Route Planning A city engineer needs to inspect the traffic signs at each street intersection of a neighborhood. The engineer has drawn a graph to represent the neighborhood, where the edges represent the streets and the vertices correspond to street intersections. Would the most efficient route to drive correspond to an Euler circuit, a Hamiltonian circuit, or neither? (The engineer must return to the starting location when finished.) Explain your answer. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.2, Problem 32ES
Textbook Problem
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## Route Planning A city engineer needs to inspect the traffic signs at each street intersection of a neighborhood. The engineer has drawn a graph to represent the neighborhood, where the edges represent the streets and the vertices correspond to street intersections. Would the most efficient route to drive correspond to an Euler circuit, a Hamiltonian circuit, or neither? (The engineer must return to the starting location when finished.) Explain your answer.

To determine

To find if the most efficient route to drive corresponds to an Euler circuit, a Hamiltonian circuit, or neither.

### Explanation of Solution

Given information:

Given, a city engineer needs to inspect the traffic signs at each street intersection of a neighborhood.

The engineer has drawn a graph to represent the neighborhood, where the edges represent the streets and the vertices correspond to street intersections.

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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