Generalized Petersen Graphs up to n=10 (synthwave; enumeration)

This synthwave enumeration shows the the Generalized Petersen Graphs G(n,k) for all n from n=4 to n=10. Can you guess how they are constructed? If you want to know more, check out the Wikipedia entry on the graphs:

If you like this video, check out my others and consider subscribing. Thanks!

0:00 : Start
00:12 : n = 4
00:22 : n = 5
00:45 : n = 6
01:08 : n = 7
01:42 : n = 8
02:17 : n = 9
03:03 : n = 10
03:52 : all graphs on same screen

#petersengraphs #graphs #counting #count #mathvideo​ #math​ #mtbos​ #manim​ #animation​​​ #iteachmath #mathematics #discretemath #combinatorics #enumeration #synthwave

To learn more about animating with manim, check out:
_________________________________________

[dudewaldo]

Second video of yours I've watched, they are gorgeous!

[MathwithWaqasShah]

great video dear. keep up the good work

[Tezhut]

Good stuff, and good job again. I'm also impressed by the frequency of your uploads!
Very tiny note of feedback: I think it would feel more smooth (natural?) if you left the text 'n = x' on the screen when it doesn't change. So when transitioning from n = 7 k =1 to n = 7 to k = 2, only the k part fades out and in.
But hey, whatever!

[mounibmekhilef]

like it much. are you asking how they are generated ? it appears as straightforward. Wont be ridiculous by posting the core thing which is actually what $k$ stands for. Am I wrong ?

[sachs]

For n = 7, the graphs with k = 2 and k = 3 are isomorphic.
For n = 9, the graphs with k = 2 and k = 4 are isomorphic.
So 17 different graphs up to isomorphism here.