Your data matches 17 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000987
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000987: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 5
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
Description
The number of positive eigenvalues of the Laplacian matrix of the graph. This is the number of vertices minus the number of connected components of the graph.
Matching statistic: St001120
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001120: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 5
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
Description
The length of a longest path in a graph.
Matching statistic: St001725
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001725: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2 = 1 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
Description
The harmonious chromatic number of a graph. A harmonious colouring is a proper vertex colouring such that any pair of colours appears at most once on adjacent vertices.
Matching statistic: St000937
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
St000937: Integer partitions ⟶ ℤResult quality: 75% ●values known / values provided: 80%●distinct values known / distinct values provided: 75%
Values
['A',1]
 => ([],1)
 => ([],1)
 => [1]
 => ? = 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => [2,1,1]
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => [2,1,1,1,1]
 => 5
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => 5
Description
The number of positive values of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation $S^{(2,2)}$ are $2$ on the conjugacy classes $(4)$ and $(2,2)$, $0$ on the conjugacy classes $(3,1)$ and $(1,1,1,1)$, and $-1$ on the conjugacy class $(2,1,1)$. Therefore, the statistic on the partition $(2,2)$ is $2$.
Matching statistic: St000454
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 75%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ? = 5
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5
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.
Matching statistic: St001621
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ Lattices
Mp00197: Lattices —lattice of congruences⟶ Lattices
St001621: Lattices ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 75%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 5
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ? = 5
Description
The number of atoms of a lattice. An element of a lattice is an '''atom''' if it covers the least element.
Matching statistic: St001638
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001638: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 75%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 5
Description
The book thickness of a graph. The book thickness (or pagenumber, or stacknumber) of a graph is the minimal number of pages required for a book embedding of a graph.
Matching statistic: St001644
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001644: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 75%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ? = 5
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5
Description
The dimension of a graph. The dimension of a graph is the least integer $n$ such that there exists a representation of the graph in the Euclidean space of dimension $n$ with all vertices distinct and all edges having unit length. Edges are allowed to intersect, however.
Matching statistic: St001742
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001742: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 75%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 5
Description
The difference of the maximal and the minimal degree in a graph. The graph is regular if and only if this statistic is zero.
Matching statistic: St001812
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001812: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 75%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => ([(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
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 5
Description
The biclique partition number of a graph. The biclique partition number of a graph is the minimum number of pairwise edge disjoint complete bipartite subgraphs so that each edge belongs to exactly one of them. A theorem of Graham and Pollak [1] asserts that the complete graph $K_n$ has biclique partition number $n - 1$.
The following 7 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000741The Colin de Verdière graph invariant. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001330The hat guessing number of a graph. St001391The disjunction number of a graph. St001642The Prague dimension of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St001738The minimal order of a graph which is not an induced subgraph of the given graph.