Solving K Complete Graph: Edges & Vertices Ratio

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SUMMARY

The discussion centers on deriving the formula for the number of edges in a complete graph Kn, which is established as n/2 * (n-1). Participants explore the ratio of edges to vertices as n increases, with the ratio expressed as n/(n/2*(n-1)). Additionally, the conversation touches on the necessary relationship between edges and vertices for a graph G that can be represented on a torus, indicating a deeper exploration of graph theory concepts.

PREREQUISITES
  • Understanding of complete graphs and their properties
  • Familiarity with graph theory terminology, including edges and vertices
  • Basic knowledge of mathematical ratios and formulas
  • Concept of graph representation on different surfaces, such as a torus
NEXT STEPS
  • Research the properties of complete graphs and their edge formulas
  • Study the implications of increasing n on the edges-to-vertices ratio
  • Explore graph representation on surfaces, focusing on toroidal graphs
  • Learn about the mathematical principles behind ratios in graph theory
USEFUL FOR

Students and professionals in mathematics, computer science, and graph theory, particularly those interested in the properties of complete graphs and their applications in topology.

chaotixmonjuish
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I'm having problems taking a stab at this question:

Find a formula for the number of edges in Kn. What happens to the ratio of edges to verticies as n increases?

Formula: n/2 * (n-1)
Ratio: this is the part I can't figure out. I assumed the ration is n/(n/2*(n-1))

Give a brief verbal argument that employs this rule of inference?


Find a necessary relationship between the number of edges and number of vertices's of a graph G if it can be represented on a Torus?

The last two parts have completely stumped me.
 
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Doesn't the ratio of x to y mean \frac{x}{y}?
 

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