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Identifier

St000777: Graphs ⟶ ℤ

Values

([],1) => 1

([(0,1)],2) => 2

([(0,2),(1,2)],3) => 3

([(0,1),(0,2),(1,2)],3) => 2

([(0,3),(1,3),(2,3)],4) => 3

([(0,3),(1,2),(2,3)],4) => 4

([(0,3),(1,2),(1,3),(2,3)],4) => 4

([(0,2),(0,3),(1,2),(1,3)],4) => 3

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(0,4),(1,4),(2,4),(3,4)],5) => 3

([(0,4),(1,4),(2,3),(3,4)],5) => 5

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 4

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 5

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 5

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

([(0,4),(1,3),(2,3),(2,4)],5) => 5

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 5

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 4

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 3

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 5

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 5

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 5

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 5

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 3

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 3

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 6

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 6

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 6

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 6

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 6

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 4

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 6

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 6

([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 4

([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 6

([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 6

([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 6

([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 6

([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 5

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 6

([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 6

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6

([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 6

([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 5

([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 6

([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 5

([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 4

([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 5

([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 6

([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 6

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 6

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 6

([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 4

([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4

([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 4

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

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Description

The number of distinct eigenvalues of the distance Laplacian of a connected graph.

Code

def distance_laplacian(G):
    if not G.is_connected():
        return
    D = G.distance_matrix()
    T = [sum(row) for row in D]
    return diagonal_matrix(T)-D

def statistic(G):
    return len(set(distance_laplacian(G).eigenvalues()))

Created

Apr 12, 2017 at 11:54 by Martin Rubey

Updated

Apr 12, 2017 at 11:54 by Martin Rubey