Graphs And Polyhedra

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Concept Map

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Textbook

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

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
Introduction to Graph Theory, By Douglas B.West/

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.

Activities

Activity No #1

Construction of regular polyhedrons

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=[[Graphs_And_Polyhedra_concept4_activity1#Activity_-_Transversable_Networks| 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.

Activities

Activity No #1 Construction of regular octahedron and recognising th elements of Polyhedrons
Activity No #2 Polyhedra_Elements

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 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.


koning4.jpg


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

For solution click here

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