Chapter I - Respecting the Rules

In the first chapter, we discuss the "number of edges that touch a vertex." This number is called the "degree" of the vertex. The groups that the COPS organizers wanted to create needed to include 15 vertices of degree 7. A well-known property in graph theory is that the total of the degrees of all the vertices is always an even number, because this total is equal to twice the number of edges in the graph. So Manori could easily demonstrate that the desired groupings were impossible, because the total of the degrees of all the vertices in a group would be equal to 7 x 15 = 105, which is not an even number.

Teaching notes - Basic Definitions and Concepts

 

• Home
• Chapter I
  Respecting the Rules
• Chapter II
  The Villas of the Bellevue
• Chapter III
  The Case of the Missing Files
• Chapter IV
  The Case of the Hidden Inheritance
• Chapter V
  An Unhappy Employee
• Chapter VI
  The Case of the Runaway Mouse
• Chapter VII
  The Case of the Hooded Man
• Chapter VIII
  The Getaway Car
• Chapter IX
  The Sudoku Apprentice
• Bibliography

Home :: Chapter I Respecting the Rules :: Chapter II The Villas of the Bellevue :: Chapter III The Case of the Missing Files :: Chapter IV The Case of the Hidden Inheritance :: Chapter V An Unhappy Employee :: Chapter VI The Case of the Runaway Mouse :: Chapter VII The Case of the Hooded Man :: Chapter VIII The Getaway Car :: Chapter IX The Sudoku Apprentice :: Bibliography