- FindStat

edit this statistic or download as text // json

Identifier

St000723: Graphs ⟶ ℤ

Values

([],1) => 1

([],2) => 2

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

([],3) => 3

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

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

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

([],4) => 4

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

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

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

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

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

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

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

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

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

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

([],5) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 1

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

([(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) => 1

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

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

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

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

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

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

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

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

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

([],6) => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => 3

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

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

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

([(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) => 4

([(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) => 1

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

([(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) => 1

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

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

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

>>> Load all 1220 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The maximal cardinality of a set of vertices with the same neighbourhood in a graph.
The set of so called mating graphs, for which this statistic equals $1$, is enumerated by [1].

References

[1] Number of n-node unlabeled graphs without endpoints (i.e., no nodes of degree 1). OEIS:A004110

Code

def statistic(G):
    t = dict()
    for v in G:
        N = Set(G[v])
        t[N] = t.get(N, 0) + 1
    return max(t.values())

Created

Mar 26, 2017 at 21:07 by Martin Rubey

Updated

Jan 18, 2019 at 10:04 by Martin Rubey