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8. Does the following graph have an Euler path? Why or why not? KAJES

8. Does the following graph have an Euler path? Why or why not? KAJES

Advanced Engineering Mathematics
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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**Question 8**: Does the following graph have an Euler path? Why or why not? **Graph Description**: The graph consists of connected line segments that form the letters "CUBS". Each letter is constructed using vertices (represented by dots) and edges (represented by lines connecting the dots). **Detailed Explanation**: - **Letter "C"**: - Vertices: 6 - Edges between vertices form an open shape resembling the letter "C". - **Letter "U"**: - Vertices: 4 - A shape resembling "U" with two vertical lines connecting to a horizontal bottom line. - **Letter "B"**: - Vertices: 6 - The letter "B" is formed by two loops vertically connected by a central vertical line. - **Letter "S"**: - Vertices: 5 - A zig-zag shape forms the letter "S". **Euler Path Explanation**: An Euler path is a path in a graph that visits every edge exactly once. A graph will have an Euler path if it has exactly 0 or 2 vertices of odd degree. Counting the degree of each vertex in this graph helps to determine the presence of an Euler path. **Conclusion**: To determine the existence of an Euler path, check the degree of each vertex: - For vertices with odd degrees, the graph should have exactly 0 or 2 to have an Euler path. Analyzing the graph visually for vertex degrees would allow a determination of whether an Euler path exists in this case.
Transcribed Image Text:**Question 8**: Does the following graph have an Euler path? Why or why not? **Graph Description**: The graph consists of connected line segments that form the letters "CUBS". Each letter is constructed using vertices (represented by dots) and edges (represented by lines connecting the dots). **Detailed Explanation**: - **Letter "C"**: - Vertices: 6 - Edges between vertices form an open shape resembling the letter "C". - **Letter "U"**: - Vertices: 4 - A shape resembling "U" with two vertical lines connecting to a horizontal bottom line. - **Letter "B"**: - Vertices: 6 - The letter "B" is formed by two loops vertically connected by a central vertical line. - **Letter "S"**: - Vertices: 5 - A zig-zag shape forms the letter "S". **Euler Path Explanation**: An Euler path is a path in a graph that visits every edge exactly once. A graph will have an Euler path if it has exactly 0 or 2 vertices of odd degree. Counting the degree of each vertex in this graph helps to determine the presence of an Euler path. **Conclusion**: To determine the existence of an Euler path, check the degree of each vertex: - For vertices with odd degrees, the graph should have exactly 0 or 2 to have an Euler path. Analyzing the graph visually for vertex degrees would allow a determination of whether an Euler path exists in this case.
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