Is it possible to know the corresponding graph labeling after using "relabel()"?

asked 2020-09-07 21:38:05 +0100

Anonymous

updated 2020-12-18 09:20:07 +0100

tmonteil
27413 ●31 ●204 ●517 http://wiki.sagemath.o...

I am trying to generate the following cayley graph

G=AlternatingGroup(5)
S=[(1,2,3),(1,2,4),(1,2,5)]
C=G.cayley_graph(generators=S, simple=True)
U=C.to_undirected()
U.vertices()

[(), (3,4,5), (3,5,4), (2,3)(4,5), (2,3,4), (2,3,5), (2,4,3), (2,4,5), (2,4)(3,5), (2,5,3), (2,5,4), (2,5)(3,4), (1,2)(4,5), (1,2)(3,4), (1,2)(3,5), (1,2,3), (1,2,3,4,5), (1,2,3,5,4), (1,2,4,5,3), (1,2,4), (1,2,4,3,5), (1,2,5,4,3), (1,2,5), (1,2,5,3,4), (1,3,2), (1,3,4,5,2), (1,3,5,4,2), (1,3)(4,5), (1,3,4), (1,3,5), (1,3)(2,4), (1,3,2,4,5), (1,3,5,2,4), (1,3)(2,5), (1,3,2,5,4), (1,3,4,2,5), (1,4,5,3,2), (1,4,2), (1,4,3,5,2), (1,4,3), (1,4,5), (1,4)(3,5), (1,4,5,2,3), (1,4)(2,3), (1,4,2,3,5), (1,4,2,5,3), (1,4,3,2,5), (1,4)(2,5), (1,5,4,3,2), (1,5,2), (1,5,3,4,2), (1,5,3), (1,5,4), (1,5)(3,4), (1,5,4,2,3), (1,5)(2,3), (1,5,2,3,4), (1,5,2,4,3), (1,5,3,2,4), (1,5)(2,4)]

Here, I used the "relabel()" function and I got the following vertices

U.relabel()
V= U.vertices()
V

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59]

Is it possible to know the corresponding labels? Like for example what is the corresponding permutation for 0?

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sage: U.relabel(return_map=True) {(): 0, (1,5,4,3,2): 1, (1,4,5,3,2): 2, (1,3,2): 3, (1,2,5,4,3): 4, (2,4,5): 5, (1,5)(2,3): 6, (1,4,3,2,5): 7, (1,3,2,4,5): 8, (1,2,3): 9, (2,3,5): 10, (1,5)(3,4): 11, (1,4,5): 12, (1,3,5): 13, (1,2)(3,4): 14, (2,5,4): 15, (1,5,3,2,4): 16, (1,4)(2,3): 17, (1,3,2,5,4): 18, (1,2,4,5,3): 19, (3,5,4): 20, (1,5,3,4,2): 21, (1,4,2): 22, (1,3,5,4,2): 23, (1,2,5,3,4): 24, (2,4,3): 25, (1,5,4,2,3): 26, (1,4,2,5,3): 27, (1,3)(2,4): 28, (1,2,3,5,4): 29, (2,3)(4,5): 30, (1,5,3): 31, (1,4,3): 32, (1,3)(4,5): 33, (1,2)(3,5): 34, (2,5)(3,4): 35, (1,5)(2,4): 36, (1,4,2,3,5): 37, (1,3,4,2,5): 38, (1,2,4): 39, (3,4,5): 40, (1,5,2): 41, (1,4,3,5,2): 42, (1,3,4,5,2): 43, (1,2,5): 44, (2,4)(3,5): 45, (1,5,2,3,4): 46, (1,4)(2,5): 47, (1,3,5,2,4): 48, (1,2,3,4,5): 49, (2,3,4): 50, (1,5,4): 51, (1,4)(3,5): 52, (1,3,4): 53, (1,2)(4,5): 54, (2,5,3): 55, (1,5,2,4,3): 56, (1,4,5,2,3): 57, (1,3)(2,5): 58, (1,2,4,3,5): 59}

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Is it possible to know the corresponding graph labeling after using "relabel()"?

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