### Theory NO. 5 : Fibbonacci strikes again!

18Feb09

Today, I noticed an amazing and worth memorizing thing. I turns out that fibbonacci series shows up also in graph theory in one of the simplest graphs:

Where’s Fibbonacci hiden here? Well, the graph can be represented as a folowing matrix:

By multiplying the matrix by itself and using induction we get:

Filed under: Mathematics, Science, Theory | 6 Comments

I haven’t got how does the matrix represent the Graph??

The matrix is the representation of the graph in the simplest posible way:

The index of any column or row represents a verticle, and if then it means that between verticles and exists a path (edge).

It’s also easy to conclude that if a vericle has a loop, then it has 1 in on axis.

When you’ll multiply matrix by itself 2 times, then numbers in the matrix represent the number of paths which length is 2 between choosen 2 verticles.

When you’ll multiply matrix by itself 3 times, then numbers in the matrix represent the number of paths which length is 3 between choosen 2 verticles.

ooh Graph .. I got it now :D

I was thinking in it as a Circle and line :)

Thanks ;)

Maybe you’ll analyse some topology and share your insights?

Just passing by.Btw, your website have great content!

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