Math Problem Statement

An employee must check the proper functioning of all this neighbourhood's traffic lights located at each intersection. Determine if possible the route he can take if each traffic light is passed only once: 1. Without going back to the starting point. 2. With going back to the starting point. Also, is it possible to take each street only once? Explain.

Solution

The question requires analyzing the directed graph to determine if an Eulerian path or circuit exists. Let’s break it down:

Part a:

1. Without going back to the starting point:

To determine if it’s possible to traverse

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Math Problem Analysis

Mathematical Concepts

Graph Theory
Eulerian Paths
Eulerian Circuits

Formulas

An Eulerian path exists if exactly 0 or 2 vertices have odd degrees.
An Eulerian circuit exists if all vertices have even degrees.

Theorems

Euler's Theorem for Directed Graphs

Suitable Grade Level

Grades 10-12

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