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Your data matches 47 different statistics following compositions of up to 3 maps.
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Matching statistic: St000928
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Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000928: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000928: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
=> ([],1)
=> [2]
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> [3,2]
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> [4,2]
=> 1
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> [6,2]
=> 0
Description
The sum of the coefficients of the character polynomial of an integer partition.
The definition of the character polynomial can be found in [1].
Matching statistic: St001354
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(load all 2 compositions to match this statistic)
Values
['A',1]
=> ([],1)
=> ([],1)
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 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
Description
The number of series nodes in the modular decomposition of a graph.
Matching statistic: St000286
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(load all 4 compositions to match this statistic)
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2 = 1 + 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 2 = 1 + 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)
=> 1 = 0 + 1
Description
The number of connected components of the complement of a graph.
The complement of a graph is the graph on the same vertex set with complementary edges.
Matching statistic: St000274
Values
['A',1]
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],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)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
Description
The number of perfect matchings of a graph.
A matching of a graph $G$ is a subset $F \subset E(G)$ such that no two edges in $F$ share a vertex in common. A perfect matching $F'$ is then a matching such that every vertex in $V(G)$ is incident with exactly one edge in $F'$.
Matching statistic: St000552
Values
['A',1]
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 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)
=> 0
Description
The number of cut vertices of a graph.
A cut vertex is one whose deletion increases the number of connected components.
Matching statistic: St001071
Values
['A',1]
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],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)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
Description
The beta invariant of the graph.
The beta invariant was introduced by Crapo [1] for matroids. For graphs with $n$ vertices the beta invariant is
$$\beta(G) = (-1)^{n-c}\sum_{S\subseteq E} (-1)^{|S|} (n-c(S)),$$
where $c(S)$ is the number of connected components of the subgraph of $G$ with edge set $S$.
For graphs with at least one edge the beta invariant equals the absolute value of the derivative of the chromatic polynomial at $1$. [2]
The beta invariant also coincides with the coefficient of the monomial $x$, and also with the coefficient of the monomial $y$, of the Tutte polynomial.
Matching statistic: St001341
Values
['A',1]
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],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)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
Description
The number of edges in the center of a graph.
The center of a graph is the set of vertices whose maximal distance to any other vertex is minimal. In particular, if the graph is disconnected, all vertices are in the certer.
Matching statistic: St001357
Values
['A',1]
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],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)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
Description
The maximal degree of a regular spanning subgraph of a graph.
A $k$-regular spanning subgraph of a graph is also known as $k$-factor. This statistic is the largest $k$ such that the graph has a $k$-factor.
Matching statistic: St001689
Values
['A',1]
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 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)
=> 0
Description
The number of celebrities in a graph.
A celebrity is a vertex such that more than half of its neighbours have smaller degree.
Matching statistic: St001702
Values
['A',1]
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],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)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
Description
The absolute value of the determinant of the adjacency matrix of a graph.
The following 37 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001783The number of odd automorphisms of a graph. St000287The number of connected components of a graph. St000363The number of minimal vertex covers of a graph. St000553The number of blocks of a graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000916The packing number of a graph. St001342The number of vertices in the center of a graph. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001463The number of distinct columns in the nullspace of a graph. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000095The number of triangles of a graph. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000454The largest eigenvalue of a graph if it is integral. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. St001575The minimal number of edges to add or remove to make a graph edge transitive. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000450The number of edges minus the number of vertices plus 2 of a graph. St000455The second largest eigenvalue of a graph if it is integral. St000741The Colin de Verdière graph invariant. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001330The hat guessing number of a graph. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001642The Prague dimension of a graph. St001720The minimal length of a chain of small intervals in a lattice. St001734The lettericity of a graph. St001812The biclique partition number of a graph. St000822The Hadwiger number of the graph. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
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