N-Cube graph: различия между версиями
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'''<math>n</math>-Cube graph''' - | '''<math>n</math>-Cube graph''' — ''[[куб n-мерный|куб <math>n</math>-мерный]].'' | ||
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 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, undirected graph, nonoriented graph|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>. | ||
\in \{0,1\}, \ | The '''<math>n</math>-cube graph''' is a ''[[regular graph]]'' with a degree <math>n-1</math>. | ||
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 | Other names are ''[[Hypercube]]'', ''[[n-Dimensional hypercube|<math>n</math>-Dimensional hypercube]]''. | ||
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>. | |||
Версия от 13:02, 13 ноября 2019
[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].
Other names are Hypercube, [math]\displaystyle{ n }[/math]-Dimensional hypercube.