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N-Cube graph: различия между версиями
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Glk (обсуждение | вклад) (Новая страница: «'''<math>n</math>-Cube graph''' --- куб <math>n</math>-мерный. Consider the set <math>Q^{n} = \{(x_{1}, x_{2}, \ldots, x_{n})| \; x_{i} \in \{0,1\}, \: i …») |
ALEXM (обсуждение | вклад) Нет описания правки |
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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\}, | \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>. | ||