Graphs And Polyhedra
| Philosophy of Mathematics |
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Concept Map
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Textbook
Additional Information
Useful websites
Wikipedia page for Graph Theory
For More Informations on Platonic Solids
Reference Books
Teaching Outlines
- 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
Concept
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.
Activities
- Activity No #1
Introduction to Graphs
- Activity No #2
Concept #
Learning objectives
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
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. This is equivalent to asking if the multigraph on four nodes and seven edges (right figure) has an Eulerian cycle. This problem was answered in the negative by Euler (1736), and represented the beginning of graph theory.
Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html
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