# Graphs And Polyhedra

Philosophy of Mathematics |

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# Concept Map

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# Textbook

# Additional Information

More on Networks

Extending Graph Theory

## Useful websites

Wikipedia page for Graph Theory

For More Informations on Platonic Solids

For interactive Platonic Solids

## Reference Books

Click here for DSERT 10 th Text book chapter Graph Theory

Introduction to Graph Theory, By Douglas B.West/

# 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

Here we should remember in any Graph a point which is not represented by letter cannot be considered as NODE

### 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

Construction of regular polyhedrons

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

*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
Verification of Euler's Formula for Graphs

Activity No #2 Activity on verification of eulers formula

## Concept # 4 Traversibility of a graph

### Learning objectives

- To Identify even order node
- To Identify Odd order node
- Condition for Traversibility
- Condition for Non- Traversibility of 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 Transversable_Networks

Activity No #2 Eulers formula verification

## Concept # 5 Shapes of Polyhedrons

### Learning objectives

- Recognize regular and irregular polyhedron
- Can write differences between regular and irregular polyhedron

### Notes for teachers

*there can only be 5 platonic polyhedrons.*

# Poly Hydrens

## Definition

### Activities

Activity No #1
Construction of regular octahedron and recognising th elements of Polyhedrons

Activity No #2
Polyhedra_Elements
[1]

## Concept # 6 Elements of Polyhedrons

### Learning objectives

- Recognizes vertexes faces and edges of a polyhedron
- Can count number of vertexes faces and edges of a polyhedron

### Notes for teachers

### Activities

Activity No #1
Construction of regular octahedron and recognising th elements of Polyhedrons

Activity No #2
Polyhedra_Elements

## Concept # 7 Euler's Formula for Polyhedrons

### Learning objectives

- Can count number of vertexes faces and edges of a polyhedron
- Verifies Euler's formula for a given polyhedron

### Notes for teachers

### Activities

Activity No #1 Activity on Eulers Theorem

Activity No #2 Work sheet on Verification of Eulers Formula for Ployhedrons

# Assessment activities for CCE

Check your basic knowledge on Polyhedrons

| Why there are only 5 platonic solids?

# 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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