# Difference between revisions of "Graphs And Polyhedra"

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# Concept Map

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

# Textbook

1. Karnataka text book for Class 10, Chapter 17 - Graphs And Polyhedra
1. NCERT book on Graphs

# Teaching Outlines

## Concept #1 Representation of a Graph

### Learning objectives

1. To define what is node.
2. to define what is arc
3. To define what is Region
4. 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

1. To identify Plane Graph
2. 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.

Activity No #1

Activity No #2

## Concept #3 Eulers formula for graph

### Learning objectives

1. Generalization of Euler's formula
2. 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

1. To Identify even order node
2. To Identify Odd order node
3. Condition for Traversibility
4. 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

1. Recognize regular and irregular polyhedron
2. 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

1. Recognizes vertexes faces and edges of a polyhedron
2. Can count number of vertexes faces and edges of a polyhedron

### 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 octahedron and recognising th elements of Polyhedrons
Activity No #2 Polyhedra_Elements

## Concept # 7 Euler's Formula for Polyhedrons

### Learning objectives

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

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

# 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