Please show all steps and explain! **Graph Theory Course: Eulerian Walks****Introduction to Eulerian Walks:**An Eulerian walk (or Eulerian trail) is a trail in a graph that visits every edge exactly once. Determining whether a given graph has an Eulerian walk, and finding such a walk when it exists, are classic problems in graph theory.**Problem Statement:**Find an Eulerian walk in the graph depicted in Figure 3.**Graph Description:**The graph presented in Figure 3 consists of seven vertices, labeled $ v_1 $, $ v_2 $, $ v_3 $, $ v_4 $, $ v_5 $, $ v_6 $, and $ v_7 $, with edges connecting the vertices as follows:- $ v_1 $ is connected to $ v_2 $, $ v_3 $, and $ v_4 $.- $ v_2 $ is connected to $ v_1 $, $ v_3 $, $ v_4 $, and $ v_6 $.- $ v_3 $ is connected to $ v_1 $, $ v_2 $, and $ v_5 $.- $ v_4 $ is connected to $ v_1 $, $ v_2 $, $ v_5 $, and $ v_6 $.- $ v_5 $ is connected to $ v_3 $, $ v_4 $, $ v_6 $, and $ v_7 $.- $ v_6 $ is connected to $ v_2 $, $ v_4 $, $ v_5 $, and $ v_7 $.- $ v_7 $ is connected to $ v_5 $ and $ v_6 $.**Visual Representation:**The graph in Figure 3 can be described as follows:- **Vertices:** Represented by black dots labeled from $ v_1 $ to $ v_7 $.- **Edges:** Connecting lines between the vertices demonstrating the relationships (edges) between them.**Objective:**The objective is to find a walk through the graph such that each edge is visited exactly once. This is the classic Eulerian walk problem.**Analysis:**To determine if an Eulerian walk exists in this graph, the following rules must be considered:1. The graph must be connected

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Answered: nd an Eulerian walk in Figure 3. V5 V3…

Math

Advanced Math

nd an Eulerian walk in Figure 3. V5 V3 V6 V2 V1 Figure 3: Graph for Problem 3

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please show all steps and explain!

**Graph Theory Course: Eulerian Walks**

**Introduction to Eulerian Walks:**
An Eulerian walk (or Eulerian trail) is a trail in a graph that visits every edge exactly once. Determining whether a given graph has an Eulerian walk, and finding such a walk when it exists, are classic problems in graph theory.

**Problem Statement:**
Find an Eulerian walk in the graph depicted in Figure 3.

**Graph Description:**
The graph presented in Figure 3 consists of seven vertices, labeled $ v_1 $, $ v_2 $, $ v_3 $, $ v_4 $, $ v_5 $, $ v_6 $, and $ v_7 $, with edges connecting the vertices as follows:

- $ v_1 $ is connected to $ v_2 $, $ v_3 $, and $ v_4 $.
- $ v_2 $ is connected to $ v_1 $, $ v_3 $, $ v_4 $, and $ v_6 $.
- $ v_3 $ is connected to $ v_1 $, $ v_2 $, and $ v_5 $.
- $ v_4 $ is connected to $ v_1 $, $ v_2 $, $ v_5 $, and $ v_6 $.
- $ v_5 $ is connected to $ v_3 $, $ v_4 $, $ v_6 $, and $ v_7 $.
- $ v_6 $ is connected to $ v_2 $, $ v_4 $, $ v_5 $, and $ v_7 $.
- $ v_7 $ is connected to $ v_5 $ and $ v_6 $.

**Visual Representation:**
The graph in Figure 3 can be described as follows:
- **Vertices:** Represented by black dots labeled from $ v_1 $ to $ v_7 $.
- **Edges:** Connecting lines between the vertices demonstrating the relationships (edges) between them.

**Objective:**
The objective is to find a walk through the graph such that each edge is visited exactly once. This is the classic Eulerian walk problem.

**Analysis:**
To determine if an Eulerian walk exists in this graph, the following rules must be considered:
1. The graph must be connected

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