Identifier
Values
[1] => ([],1) => ([],1) => ([],1) => 1
[2] => ([],2) => ([],1) => ([],1) => 1
[1,2] => ([(1,2)],3) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[3] => ([],3) => ([],1) => ([],1) => 1
[1,3] => ([(2,3)],4) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[2,2] => ([(1,3),(2,3)],4) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[4] => ([],4) => ([],1) => ([],1) => 1
[1,4] => ([(3,4)],5) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[2,3] => ([(2,4),(3,4)],5) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[3,2] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[5] => ([],5) => ([],1) => ([],1) => 1
[1,5] => ([(4,5)],6) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[2,4] => ([(3,5),(4,5)],6) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[3,3] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[6] => ([],6) => ([],1) => ([],1) => 1
[1,6] => ([(5,6)],7) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[2,5] => ([(4,6),(5,6)],7) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[3,4] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
[7] => ([],7) => ([],1) => ([],1) => 1
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Description
The pebbling number of a connected graph.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
de-duplicate
Description
The de-duplicate of a graph.
Let G=(V,E) be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods {Nv|v∈V} of G, and has an edge (Na,Nb) between two vertices if and only if (a,b) is an edge of G. This is well-defined, because if Na=Nc and Nb=Nd, then (a,b)∈E if and only if (c,d)∈E.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
Let G=(V,E) be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods {Nv|v∈V} of G, and has an edge (Na,Nb) between two vertices if and only if (a,b) is an edge of G. This is well-defined, because if Na=Nc and Nb=Nd, then (a,b)∈E if and only if (c,d)∈E.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
Map
complement
Description
The complement of a graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
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