- FindStat

Identifier

Mp00259: Graphs —vertex addition⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000302: Graphs ⟶ ℤ

Values

([],1) => ([],2) => ([],1) => 0
([],2) => ([],3) => ([],1) => 0
([],3) => ([],4) => ([],1) => 0
([],4) => ([],5) => ([],1) => 0
([],5) => ([],6) => ([],1) => 0
([],6) => ([],7) => ([],1) => 0

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$F_{1} = 1$

Description

The determinant of the distance matrix of a connected graph.

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

$\{N_v | v \in V\}$ of

$G$ , and has an edge

$(N_a, N_b)$ between two vertices if and only if

$(a, b)$ is an edge of

$G$ . This is well-defined, because if

$N_a = N_c$ and

$N_b = N_d$ , then

$(a, b)\in E$ if and only if

$(c, d)\in E$ .
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.

Map

vertex addition

Description

Adds a disconnected vertex to a graph.