Identifier
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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Description
The hyper-Wiener index of a connected graph.
This is
$$ \sum_{\{u,v\}\subseteq V} d(u,v)+d(u,v)^2. $$
This is
$$ \sum_{\{u,v\}\subseteq V} d(u,v)+d(u,v)^2. $$
Map
vertex addition
Description
Adds a disconnected vertex to a 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.
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.
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