Просмотр кода страницы Hamming graph

'''Hamming graph''' --- граф Хэмминга. 

Given a graph <math> = (V,E)</math>,  <math>G</math> is mathcalled '''Hamming graph''' if each vertex <math>x \in V</math>  can  be  labeled  by a word <math>a(x)</math> (of fixed length) over some
symbol set <math>\Sigma</math> such that

<math> H(a(x),a(y)) = d_{G}(x,y)</math>

for arbitrary <math>x,  y \in V</math>. Here <math>a(x)</math> is termed the address of <math>x</math>,
and <math>H(a,b)</math>  stands  for  the '''Hamming distance''' of the addresses
<math>a</math> and <math>b</math>, that is, the number of positions <math>k</math> such that the <math>k</math>-th
symbol in   <math>a</math>  differs  from  the  <math>k</math>-th  symbol  in  <math>b</math>.  Futher,
<math>d_{G}(x,y)</math> denotes the length of a shortest chain in <math>G</math> between <math>x</math>
and <math>y</math>.  <math>G</math>  is  called  a  ''' binary Hamming graph''' if <math>\Sigma =
\{0,1\}</math>.