N-Cube graph: различия между версиями

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Consider the set <math>Q^{n} = \{(x_{1}, x_{2}, \ldots, x_{n})| \; x_{i}
Consider the set <math>Q^{n} = \{(x_{1}, x_{2}, \ldots, x_{n})| \; x_{i}
\in \{0,1\}, \: i = 1, \ldots, n\}</math>. For <math>u,v \in Q^{n}</math> the Hamming
\in \{0,1\}, : i = 1, \ldots, n\}</math>. For <math>u,v \in Q^{n}</math> the Hamming
distance <math>\rho(u,v)</math> is defined as the number of entries where <math>u</math> and
distance <math>\rho(u,v)</math> is defined as the number of entries where <math>u</math> and
<math>v</math> differ. An '''<math>n</math>-cube graph''' is a graph on the vertex set <math>Q^{n}</math>, where
<math>v</math> differ. An '''<math>n</math>-cube graph''' is a graph on the vertex set <math>Q^{n}</math>, where
two vertices <math>u, v</math> are ''adjacent'' iff <math>\rho(u,v) = 1</math>.
two vertices <math>u, v</math> are ''adjacent'' iff <math>\rho(u,v) = 1</math>.
The '''<math>n</math>-cube graph''' is a ''regular graph'' with a degree <math>n-1</math>.
The '''<math>n</math>-cube graph''' is a ''regular graph'' with a degree <math>n-1</math>.

Версия от 14:49, 24 сентября 2018

[math]\displaystyle{ n }[/math]-Cube graph --- куб [math]\displaystyle{ n }[/math]-мерный.

Consider the set [math]\displaystyle{ Q^{n} = \{(x_{1}, x_{2}, \ldots, x_{n})| \; x_{i} \in \{0,1\}, : i = 1, \ldots, n\} }[/math]. For [math]\displaystyle{ u,v \in Q^{n} }[/math] the Hamming distance [math]\displaystyle{ \rho(u,v) }[/math] is defined as the number of entries where [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math] differ. An [math]\displaystyle{ n }[/math]-cube graph is a graph on the vertex set [math]\displaystyle{ Q^{n} }[/math], where two vertices [math]\displaystyle{ u, v }[/math] are adjacent iff [math]\displaystyle{ \rho(u,v) = 1 }[/math]. The [math]\displaystyle{ n }[/math]-cube graph is a regular graph with a degree [math]\displaystyle{ n-1 }[/math].