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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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Statistic identifier: St001591
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Collection: Integer compositions
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Description: The number of graphs with the given composition of multiplicities of Laplacian eigenvalues.
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References:
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Code:
def mapping(G):
if G.num_verts() > 30:
raise ValueError("Graph too big for this map")
s = G.spectrum(laplacian=True)
c = []
i, o = 0, None
for v in s:
if v != o:
c.append(i)
i, o = 0, v
i += 1
c.append(i)
return Composition(c[1:])
@cached_function
def preimages(level):
print("computing preimages for level", level)
result = dict()
for el in graphs(level):
image = mapping(el)
result[image] = result.get(image, 0) + 1
return result
def statistic(x):
return preimages(x.size()).get(x, 0)
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Statistic values:
[1] => 1
[1,1] => 1
[2] => 1
[1,1,1] => 1
[1,2] => 1
[2,1] => 1
[3] => 1
[1,1,1,1] => 2
[1,1,2] => 1
[1,2,1] => 2
[1,3] => 1
[2,1,1] => 1
[2,2] => 2
[3,1] => 1
[4] => 1
[1,1,1,1,1] => 10
[1,1,1,2] => 3
[1,1,2,1] => 2
[1,1,3] => 1
[1,2,1,1] => 2
[1,2,2] => 2
[1,3,1] => 1
[1,4] => 1
[2,1,1,1] => 1
[2,1,2] => 2
[2,2,1] => 3
[2,3] => 2
[3,1,1] => 1
[3,2] => 1
[4,1] => 1
[5] => 1
[1,1,1,1,1,1] => 53
[1,1,1,1,2] => 11
[1,1,1,2,1] => 1
[1,1,1,3] => 3
[1,1,2,1,1] => 13
[1,1,2,2] => 3
[1,1,3,1] => 3
[1,1,4] => 1
[1,2,1,1,1] => 13
[1,2,1,2] => 3
[1,2,2,1] => 6
[1,2,3] => 2
[1,3,1,1] => 4
[1,3,2] => 2
[1,4,1] => 2
[1,5] => 1
[2,1,1,1,1] => 3
[2,1,1,2] => 1
[2,1,2,1] => 4
[2,1,3] => 2
[2,2,1,1] => 3
[2,2,2] => 5
[2,3,1] => 2
[2,4] => 2
[3,1,1,1] => 1
[3,1,2] => 3
[3,2,1] => 2
[3,3] => 2
[4,1,1] => 1
[4,2] => 2
[5,1] => 1
[6] => 1
[1,1,1,1,1,1,1] => 589
[1,1,1,1,1,2] => 61
[1,1,1,1,2,1] => 4
[1,1,1,1,3] => 11
[1,1,1,2,1,1] => 53
[1,1,1,2,2] => 3
[1,1,1,3,1] => 3
[1,1,1,4] => 3
[1,1,2,1,1,1] => 42
[1,1,2,1,2] => 16
[1,1,2,2,1] => 5
[1,1,2,3] => 3
[1,1,3,1,1] => 9
[1,1,3,2] => 6
[1,1,4,1] => 2
[1,1,5] => 1
[1,2,1,1,1,1] => 40
[1,2,1,1,2] => 16
[1,2,1,2,1] => 16
[1,2,1,3] => 4
[1,2,2,1,1] => 9
[1,2,2,2] => 9
[1,2,3,1] => 3
[1,2,4] => 2
[1,3,1,1,1] => 10
[1,3,1,2] => 5
[1,3,2,1] => 3
[1,3,3] => 2
[1,4,1,1] => 2
[1,4,2] => 2
[1,5,1] => 1
[1,6] => 1
[2,1,1,1,1,1] => 11
[2,1,1,1,2] => 4
[2,1,1,2,1] => 3
[2,1,1,3] => 1
[2,1,2,1,1] => 14
[2,1,2,2] => 6
[2,1,3,1] => 3
[2,1,4] => 2
[2,2,1,1,1] => 3
[2,2,1,2] => 5
[2,2,2,1] => 8
[2,2,3] => 6
[2,3,1,1] => 2
[2,3,2] => 3
[2,4,1] => 2
[2,5] => 2
[3,1,1,1,1] => 3
[3,1,1,2] => 3
[3,1,2,1] => 2
[3,1,3] => 3
[3,2,1,1] => 2
[3,2,2] => 3
[3,3,1] => 4
[3,4] => 2
[4,1,1,1] => 1
[4,1,2] => 2
[4,2,1] => 2
[4,3] => 2
[5,1,1] => 1
[5,2] => 1
[6,1] => 1
[7] => 1
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Created: Sep 12, 2020 at 09:17 by Martin Rubey
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Last Updated: Sep 12, 2020 at 09:17 by Martin Rubey