- FindStat

Identifier

Mp00250: Graphs —clique graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001704: Graphs ⟶ ℤ

Values

([(0,2),(1,2)],3) => ([(0,1)],2) => ([(0,1)],2) => 2

([(1,3),(2,3)],4) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,3),(1,2),(2,3)],4) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2

([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1)],2) => ([(0,1)],2) => 2

([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1)],2) => ([(0,1)],2) => 2

([(2,4),(3,4)],5) => ([(2,3)],4) => ([(0,1)],2) => 2

([(1,4),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(1,4),(2,3),(3,4)],5) => ([(1,3),(2,3)],4) => ([(0,1)],2) => 2

([(0,1),(2,4),(3,4)],5) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => 2

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1)],2) => 2

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1)],2) => 2

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1)],2) => 2

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1)],2) => 2

([(3,5),(4,5)],6) => ([(3,4)],5) => ([(0,1)],2) => 2

([(2,5),(3,5),(4,5)],6) => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

([(2,5),(3,4),(4,5)],6) => ([(2,4),(3,4)],5) => ([(0,1)],2) => 2

([(1,2),(3,5),(4,5)],6) => ([(2,3)],4) => ([(0,1)],2) => 2

([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,1),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(2,5),(3,4),(3,5),(4,5)],6) => ([(2,3)],4) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(2,4),(2,5),(3,4),(3,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => ([(0,1)],2) => 2

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,3)],4) => ([(0,1)],2) => 2

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,3),(2,3)],4) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(1,5),(2,4),(3,4),(3,5)],6) => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 2

([(0,1),(2,5),(3,4),(4,5)],6) => ([(1,3),(2,3)],4) => ([(0,1)],2) => 2

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,3),(2,3)],4) => ([(0,1)],2) => 2

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,3),(2,3)],4) => ([(0,1)],2) => 2

([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2

([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1)],2) => 2

([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => 2

([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => 2

([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2

([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2)],3) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2

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Description

The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph.
The deck of a graph is the multiset of induced subgraphs obtained by deleting a single vertex.
The graph reconstruction conjecture states that the deck of a graph with at least three vertices determines the graph.
This statistic is only defined for graphs with at least two vertices, because there is only a single graph of the given size otherwise.

Map

clique graph

Description

The clique graph of a graph.
The clique graph of a graph $G$ has as vertex set the set of maximal cliques $G$ and an edge between vertices corresponding to cliques that intersect.
In other words, it is the intersection graph of the maximal cliques of $G$.

Map

core

Description

The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].