Solving K Complete Graph: Edges & Vertices Ratio

  • Thread starter Thread starter chaotixmonjuish
  • Start date Start date
  • Tags Tags
    Complete Graph
AI Thread Summary
The discussion focuses on finding a formula for the number of edges in a complete graph Kn, which is given as n(n-1)/2. The participant is struggling with determining the ratio of edges to vertices as n increases, initially assuming it to be n/(n/2*(n-1)). There is confusion regarding the interpretation of the ratio and its mathematical representation. Additionally, the participant seeks a necessary relationship between edges and vertices for a graph that can be represented on a torus. Clarification on these concepts is needed to resolve the participant's questions.
chaotixmonjuish
Messages
284
Reaction score
0
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.
 
Physics news on Phys.org
Doesn't the ratio of x to y mean \frac{x}{y}?
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

Similar threads

Replies
6
Views
2K
Replies
1
Views
2K
Replies
26
Views
12K
Replies
2
Views
1K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
2
Views
2K
Back
Top