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- Beraha's conjecture, wheels, and cyclic graphs
- Zizi, Jacqueline
- A graph coloring assigns colors to the vertices of a graph in such a way that a pair of vertices joined by an edge do not get the same color. The chromatic polynomial of a graph gives the number of ways of coloring the graph with x colors. Beraha's numbers are B(n)=4*cos^2(pi/n). Tutte conjectured that there is a link between Beraha's numbers and some classes of graphs. This Demonstration shows that for a small number of vertices, it is not obvious what the connection is between the roots of the chromatic polynomial of a cyclic graph (green), the roots of the chromatic polynomial of the corresponding wheel graph (purple), and Beraha's numbers (red). However, taking more vertices clearly shows a relationship between these three sets of numbers
- Componente Curricular::Ensino Médio::Matemática
- Complex Numbers
- Discrete Mathematics
- Golden Ratio
- Educação Básica::Ensino Médio::Matemática::Geometria
- Shows Beraha's conjecture
- This demonstration needs the "MathematicaPlayer.exe" to run. Found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
- Demonstration freeware using Mathematica Player
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