- FindStat

Identifier

St000454: Graphs ⟶ ℤ

Values

=>
                            Cc0020;cc-rep
                            
                            
                            

                        ([],1)=>0
([],2)=>0
([(0,1)],2)=>1
([],3)=>0
([(1,2)],3)=>1
([(0,1),(0,2),(1,2)],3)=>2
([],4)=>0
([(2,3)],4)=>1
([(0,3),(1,2)],4)=>1
([(1,2),(1,3),(2,3)],4)=>2
([(0,2),(0,3),(1,2),(1,3)],4)=>2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3
([],5)=>0
([(3,4)],5)=>1
([(0,4),(1,4),(2,4),(3,4)],5)=>2
([(1,4),(2,3)],5)=>1
([(2,3),(2,4),(3,4)],5)=>2
([(1,3),(1,4),(2,3),(2,4)],5)=>2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,1),(2,3),(2,4),(3,4)],5)=>2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2
([(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)=>4
([],6)=>0
([(4,5)],6)=>1
([(1,5),(2,5),(3,5),(4,5)],6)=>2
([(2,5),(3,4)],6)=>1
([(3,4),(3,5),(4,5)],6)=>2
([(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,4),(2,3)],6)=>1
([(1,2),(3,4),(3,5),(4,5)],6)=>2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>3
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>3
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([],7)=>0
([(5,6)],7)=>1
([(2,6),(3,6),(4,6),(5,6)],7)=>2
([(3,6),(4,5)],7)=>1
([(4,5),(4,6),(5,6)],7)=>2
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>2
([(3,5),(3,6),(4,5),(4,6)],7)=>2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
([(1,6),(2,5),(3,4)],7)=>1
([(2,3),(4,5),(4,6),(5,6)],7)=>2
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>2
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>2
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>2
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>3
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)=>2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>2
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)=>2
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>2
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>3
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)=>2
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)=>2
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)=>2
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>3
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>3
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)=>2
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>4
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>4
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>4
([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>3
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>4
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>3
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>4
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>5
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>4
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>5
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6
                    

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 largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.

Code

def statistic(G):
    e = max([e for (e,_,_) in G.eigenvectors()])
    if e in ZZ:
        return e

Created

Apr 04, 2016 at 11:40 by Martin Rubey

Updated

Mar 23, 2017 at 20:51 by Martin Rubey