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 HGraph 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 GGraph 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. ### ConclusionBoth 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 PlanarityTo 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

In graph theory, the terms "K5" and "K33" refer to specific types of complete bipartite graphs.A…

Answered: (b) Determine which of the following…

(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

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

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Concept explainers

Strongly Connected Components

A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).

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

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