Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
(b) Determine which of the following two graphs are planar. Justify your answer and show your work. Graph H f a b Graph G b f

(b) Determine which of the following two graphs are planar. Justify your answer and show your work. Graph H f a b Graph G b f

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
See similar textbooks
icon
Related questions
Question

how to tell whether it is k5 or k33?

### Planar Graph Determination **(b) Determine which of the following two graphs are planar. Justify your answer and show your work.** #### Graph H Graph H is represented with the following vertices and edges: - **Vertices:** a, b, c, d, e, f, g - **Edges:** (a-d), (a-e), (a-f), (b-d), (b-f), (b-g), (c-d), (c-e), (c-f), (d-e), (d-f) Explanation: Graph H appears to have multiple intersecting edges, making it non-planar. It cannot be redrawn in a two-dimensional plane without some edges crossing each other. #### Graph G Graph G is represented with the following vertices and edges: - **Vertices:** a, b, c, d, e, f, g - **Edges:** (a-b), (a-c), (a-d), (a-g), (b-c), (b-e), (c-g), (c-e), (d-f), (d-g), (e-f) Explanation: Graph G also shows several intersecting edges. To determine if this graph is planar, we need to check if it can be redrawn without any edge crossings. It appears that graph G cannot be redrawn without edge crossings, making it non-planar as well. ### Conclusion Both Graph H and Graph G are non-planar graphs because there is no way to draw either of them without their edges crossing in the plane. This can be justified by examining the intersections and crossings of the edges in each graph. ### Detailed Analysis of Planarity To further solidify the analysis, we can apply Kuratowski's Theorem for planarity. A graph is planar if and only if it does not contain a subgraph that is a subdivision of \( K_5 \) (complete graph on 5 vertices) or \( K_{3,3} \) (complete bipartite graph on 6 vertices). Both given graphs, H and G, seem to embed such complex substructures, indicating their non-planarity. **Note:** If you need assistance in redrawing or further steps, make sure to follow up with a more detailed analysis or graph-redrawing tool to visually ascertain the planar nature of the given graphs. Would you like to dive deeper into the theoretical concepts or explore practical examples of planar and non-planar graphs? Feel
Transcribed Image Text:### Planar Graph Determination **(b) Determine which of the following two graphs are planar. Justify your answer and show your work.** #### Graph H Graph H is represented with the following vertices and edges: - **Vertices:** a, b, c, d, e, f, g - **Edges:** (a-d), (a-e), (a-f), (b-d), (b-f), (b-g), (c-d), (c-e), (c-f), (d-e), (d-f) Explanation: Graph H appears to have multiple intersecting edges, making it non-planar. It cannot be redrawn in a two-dimensional plane without some edges crossing each other. #### Graph G Graph G is represented with the following vertices and edges: - **Vertices:** a, b, c, d, e, f, g - **Edges:** (a-b), (a-c), (a-d), (a-g), (b-c), (b-e), (c-g), (c-e), (d-f), (d-g), (e-f) Explanation: Graph G also shows several intersecting edges. To determine if this graph is planar, we need to check if it can be redrawn without any edge crossings. It appears that graph G cannot be redrawn without edge crossings, making it non-planar as well. ### Conclusion Both Graph H and Graph G are non-planar graphs because there is no way to draw either of them without their edges crossing in the plane. This can be justified by examining the intersections and crossings of the edges in each graph. ### Detailed Analysis of Planarity To further solidify the analysis, we can apply Kuratowski's Theorem for planarity. A graph is planar if and only if it does not contain a subgraph that is a subdivision of \( K_5 \) (complete graph on 5 vertices) or \( K_{3,3} \) (complete bipartite graph on 6 vertices). Both given graphs, H and G, seem to embed such complex substructures, indicating their non-planarity. **Note:** If you need assistance in redrawing or further steps, make sure to follow up with a more detailed analysis or graph-redrawing tool to visually ascertain the planar nature of the given graphs. Would you like to dive deeper into the theoretical concepts or explore practical examples of planar and non-planar graphs? Feel
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Strongly connected components
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS