Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001828
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Mapping
St001828: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 1
([],3)
 => 3
([(1,2)],3)
 => 2
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => 4
([(2,3)],4)
 => 3
([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => 2
([(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)
 => 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => -1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => -2
([],5)
 => 5
([(3,4)],5)
 => 4
([(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3)],5)
 => 3
([(1,4),(2,3),(3,4)],5)
 => 2
([(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)
 => 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => -1
([(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)
 => -2
([(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)
 => 0
([(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)
 => 0
([(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)
 => -2
([(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)
 => -2
([(0,3),(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)],5)
 => -2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => -3
Description
The Euler characteristic of a graph. The '''Euler characteristic''' $\chi$ of a topological space is the alternating sum of the dimensions of the homology groups $$\chi(X) = \sum_{k \geq 0} (-1)^k \dim H_k(X).$$ For a finite simplicial complex, this is equal to the alternating sum $ \sum_{k\geq 0} (-1)^k f_k$ where $f_k$ the number of $k$-dimensional simplices. A (simple) graph is a simplicial complex of dimension at most one; its vertices are the 0-simplices and its edges are the 1-simplices. For a connected graph, the Euler characteristic is equal to $1 - g$ where $g$ is the cyclomatic number.