# Graphs And Polyhedra

Philosophy of Mathematics |

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# Concept Map

**Error: Mind Map file Graphs And Polyhedrons.mm not found **

# Textbook

# Additional Information

## Useful websites

Wikipedia page for Graph Theory

For More Informations on Platonic Solids

## Reference Books

Click here for DSERT 10 th Text book chapter Graph Theory

# Teaching Outlines

## Concept #1 Representation of a Graph

### Learning objectives

- To define what is node.
- to define what is arc
- To define what is Region
- To represent a Graph with node, Arc and Regions

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

- Defining a Graph, node arc and Region
- Framing Euler's Formula for graphs
- Verifying Euler's Formula N + R = A + 2 for given Plane graphs
- Drawing graphs for given N,R and A
- Identifying the Traversible graphs
- Explaining and using the condition for Traversible graphs
- defining a Polyhedra
- Framing Euler's formula for Polyhedra
- verifying Euler's formula for the given Polyhedra

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activities

Activity #1 Introduction to Graphs

Activity #2 Graph Theory

## Concept #2 Types of Graphs

### Learning objectives

- To identify Plane Graph
- To identify Non-Plane Graph

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activities

- Activity No #1
- Activity No #2

## Concept #3 Eulers formula for graph

### Learning objectives

- Generalization of Euler's formula
- Verification of Euler's formula for Networks

### Notes for teachers

### Activities

- Activity No #1
- Activity No #2

## Concept 1Representation of a graph

### Learning objectives

### Notes for teachers

### Activities

- Activity No #1
- Activity No #2

# Assessment activities for CCE

Check your basic knowledge on Polyhedrons

# Hints for difficult problems

Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began.

Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html

For solution click **here**

# Project Ideas

# Math Fun

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