please write out equations and explain/write out theorems **Problem 1:** Determine whether graphs \( G \) and \( H \) are planar or not. To show planarity, give a planar embedding. To show that a graph is not planar, use Kuratowski’s theorem.### Graph G:Graph \( G \) consists of seven vertices labeled \( a, b, c, d, e, f, \) and \( g \). The vertices are interconnected with edges forming a complete graph structure, indicating a high degree of connectivity among them.### Graph H:Graph \( H \) also has seven vertices labeled \( a, b, c, d, e, f, \) and \( g \). This graph appears more interconnected and complex, with multiple crisscrossing edges, indicating possible non-planarity.**Explanation of Planarity and Kuratowski's Theorem:**- **Planarity**: A graph is planar if it can be drawn on a plane without any edges crossing.- **Kuratowski's Theorem**: A graph is non-planar if and only if it contains a subgraph that is a subdivision of \( K_5 \) (complete graph on five vertices) or \( K_{3,3} \) (complete bipartite graph on two sets of three vertices).To determine the planarity of Graphs \( G \) and \( H \), examine whether these graphs can be redrawn without crossing edges or if they contain a subgraph homeomorphic to \( K_5 \) or \( K_{3,3} \).

Answered: Problem 1: Determine whether graphs G…

Problem 1: Determine whether graphs G and H are planar or not. To show planarity, give a planar embedding. To show that a graph is not planar, use Kuratowski's theorem. X Graph G: Graph H: b

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

please write out equations and explain/write out theorems

**Problem 1:** Determine whether graphs \( G \) and \( H \) are planar or not. To show planarity, give a planar embedding. To show that a graph is not planar, use Kuratowski’s theorem.

### Graph G:
Graph \( G \) consists of seven vertices labeled \( a, b, c, d, e, f, \) and \( g \). The vertices are interconnected with edges forming a complete graph structure, indicating a high degree of connectivity among them.

### Graph H:
Graph \( H \) also has seven vertices labeled \( a, b, c, d, e, f, \) and \( g \). This graph appears more interconnected and complex, with multiple crisscrossing edges, indicating possible non-planarity.

**Explanation of Planarity and Kuratowski's Theorem:**

- **Planarity**: A graph is planar if it can be drawn on a plane without any edges crossing.
- **Kuratowski's Theorem**: A graph is non-planar if and only if it contains a subgraph that is a subdivision of \( K_5 \) (complete graph on five vertices) or \( K_{3,3} \) (complete bipartite graph on two sets of three vertices).

To determine the planarity of Graphs \( G \) and \( H \), examine whether these graphs can be redrawn without crossing edges or if they contain a subgraph homeomorphic to \( K_5 \) or \( K_{3,3} \).

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