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Your data matches 62 different statistics following compositions of up to 3 maps.
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Matching statistic: St000636
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Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
Description
The hull number of a graph.
The convex hull of a set of vertices $S$ of a graph is the smallest set $h(S)$ such that for any pair $u,v\in h(S)$ all vertices on a shortest path from $u$ to $v$ are also in $h(S)$.
The hull number is the size of the smallest set $S$ such that $h(S)$ is the set of all vertices.
Matching statistic: St000917
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Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
Description
The open packing number of a graph.
This is the size of a largest subset of vertices of a graph, such that any two distinct vertices in the subset have disjoint open neighbourhood.
Matching statistic: St000918
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Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
Description
The 2-limited packing number of a graph.
A subset $B$ of the set of vertices of a graph is a $k$-limited packing set if its intersection with the (closed) neighbourhood of any vertex is at most $k$. The $k$-limited packing number is the largest number of vertices in a $k$-limited packing set.
Matching statistic: St001315
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Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
Description
The dissociation number of a graph.
Matching statistic: St001654
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Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
Description
The monophonic hull number of a graph.
The monophonic hull of a set of vertices $M$ of a graph $G$ is the set of vertices that lie on at least one induced path between vertices in $M$. The monophonic hull number is the size of the smallest set $M$ such that the monophonic hull of $M$ is all of $G$.
For example, the monophonic hull number of a graph $G$ with $n$ vertices is $n$ if and only if $G$ is a disjoint union of complete graphs.
Matching statistic: St001655
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Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
Description
The general position number of a graph.
A set $S$ of vertices in a graph $G$ is a general position set if no three vertices of $S$ lie on a shortest path between any two of them.
Matching statistic: St001656
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Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
Description
The monophonic position number of a graph.
A subset $M$ of the vertex set of a graph is a monophonic position set if no three vertices of $M$ lie on a common induced path. The monophonic position number is the size of a largest monophonic position set.
Matching statistic: St001318
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Values
([],1)
=> ([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> ([],6)
=> 6
Description
The number of vertices of the largest induced subforest with the same number of connected components of a graph.
Matching statistic: St001321
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Values
([],1)
=> ([],1)
=> ([],1)
=> 1
([],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,1)],2)
=> ([],2)
=> ([],2)
=> 2
([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(2,1)],3)
=> ([],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(3,4)],5)
=> ([(3,4)],5)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(3,4)],5)
=> ([(3,4)],5)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> ([],5)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> ([(3,4)],5)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> ([],6)
=> 6
Description
The number of vertices of the largest induced subforest of a graph.
Matching statistic: St000778
Values
([],1)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 1
([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 2
([(1,2)],3)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2
([(0,1),(0,2)],3)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(3,4)],5)
=> 3
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 3
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(3,4)],5)
=> 3
([(0,2),(0,3),(3,1)],4)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> 3
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(4,5)],6)
=> 4
([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(4,5)],6)
=> 4
([(0,3),(1,3),(3,2)],4)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(4,5)],6)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(3,6),(4,5)],7)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(3,6),(4,5),(5,6)],7)
=> 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(5,6)],7)
=> 5
([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(5,6)],7)
=> 5
([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ([(5,6)],7)
=> 5
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(5,6)],7)
=> 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 6
Description
The metric dimension of a graph.
This is the length of the shortest vector of vertices, such that every vertex is uniquely determined by the vector of distances from these vertices.
The following 52 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001119The length of a shortest maximal path in a graph. St001949The rigidity index of a graph. St000258The burning number of a graph. St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001363The Euler characteristic of a graph according to Knill. St001391The disjunction number of a graph. St000741The Colin de Verdière graph invariant. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St000717The number of ordinal summands of a poset. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. St001645The pebbling number of a connected graph. St000287The number of connected components of a graph. St001828The Euler characteristic of a graph. St001271The competition number of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St000454The largest eigenvalue of a graph if it is integral. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St000699The toughness times the least common multiple of 1,. St001281The normalized isoperimetric number of a graph. St001592The maximal number of simple paths between any two different vertices of a graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001875The number of simple modules with projective dimension at most 1. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000656The number of cuts of a poset. St000680The Grundy value for Hackendot on posets. St000906The length of the shortest maximal chain in a poset. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St000327The number of cover relations in a poset. St000264The girth of a graph, which is not a tree. St001060The distinguishing index of a graph. St001118The acyclic chromatic index of a graph. St001545The second Elser number of a connected graph. St000456The monochromatic index of a connected graph. St000455The second largest eigenvalue of a graph if it is integral. St000464The Schultz index of a connected graph. St000260The radius of a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000259The diameter of a connected graph. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001877Number of indecomposable injective modules with projective dimension 2. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
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