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Identifier

St001694: Graphs ⟶ ℤ

Values

([],1) => 1

([],2) => 1

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

([],3) => 1

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

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

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

([],4) => 1

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

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

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

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

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

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

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

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

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

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

([],5) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 10

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10

([],6) => 1

([(4,5)],6) => 1

([(3,5),(4,5)],6) => 3

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

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

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

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

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

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

([(3,4),(3,5),(4,5)],6) => 3

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

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

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

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

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

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

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

([(0,5),(1,5),(2,4),(3,4)],6) => 9

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

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

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

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

([(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) => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of maximal dissociation sets in a graph.

References

[1] wikipedia:Dissociation number
[2] Tu, J., Zhang, L., Du, J. On the maximum number of maximum dissociation sets in trees with given dissociation number arXiv:2103.01407

Code

def statistic(G):
    n = 0
    for k in range(G.num_verts(), 0, -1):
        for S in Subsets(G.vertices(), k):
            H = G.subgraph(vertices=S)
            if max(H.degree()) <= 1:
                n += 1
        if n > 0:
            return n
    return

Created

Mar 03, 2021 at 10:59 by Martin Rubey

Updated

Mar 03, 2021 at 10:59 by Martin Rubey