Lee Distance and Topological Properties of kary ncubes

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Lee Distance and Topological Properties of k-ary
n-cubes

• ??ts??? Ge??????
• ?.?. 113

2
??sa????

• ? k-ary n-cube ??e? ???s?µ?p????e? st?? s?ed?asµ?
  p????? s???????? ?p?????st??
• ?p?s?? ??e? ???s?µ?p??e?ta? ??a t??
  ap?te?esµat??? ep???s? ?p?????sµ?? ??aµµ????
  ???eß?a?, ?a??? ?a? µe????? pa?a?????

3
????ata??t???

• Lee Distance and the k-ary n-cube
• ?st? ??a d????sµa n??f??? ß?s?? k
• Lee weight
  
• Lee distance
  
• p.?. ??a k4, ?a? .
• ?p?stas? Hamming ?p?stas? Hamming d??
  d?a??sµ?t?? ?,? ????eta? ?? t? p????? t?? ??se??
  st?? ?p??e? ta ? ?a? ? d?af?????.

4
????ata??t???

• G??f??
• e??a? ??a? 2n-regular ???f?? p?? ap?te?e?ta? ap?
  ??µß???. ???e ??µß?? ???µ??eta? µe a???????e? n-
  ??f??? ß?s?? k, .
• ??µ? µeta?? U,V µ??? ?ta?
  µ?????eta? µ?a a?µ? µe d?? ??µß??? se ???e
  d??stas? ?a? ?ts? µ???µe ??a ??a? ???f? ßa?µ??
  . ?? ???t???te?? µ???p?t? µeta?? d?? ??µß??
  U ?a? V ??e? µ???? .
• ???µet??? ?? D ? d??µet??? t?? t?te
  
• Links ?? L t? s??????? p????? t?? Links se ??a?
  , kgt2, t?te

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????ata??t???

• Surface Area ?? t? p????? t?? ????f??
  se ??a? t?? ?p???? ? ap?stas? ap? ??a? d????
  ??µß? e??a? a???ß?? d, ?p?? dltk/2, t?te t?
  e??a? ? ep?f??e?a (surface area) µ?a? sfa??a?
  a?t??a? d.
• Volume ?? t? p????? t?? ????f?? se ??a?
  t?? ?p???? ? ap?stas? ap? ??a? d???? ??µß?
  e??a? µ????te?? ? ?s? µe d, ?p?? dltk/2, t?te t?
  e??a? ? ????? (volume) µ?a? sfa??a?
  a?t??a? d.

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G???µe?? G??f??

• ?????t?? , ,.,
  ????ete t?
• sta???t? ????µe?? t?? ,p??
  s?µß????ete
• ?? ? ???f?? , ?p??
  ?a?
• k-ary cycle ????eta? ?? ? ???f?? p?? ap?te?e?ta?
  ap? k ??µß??? ?a? k a?µ??. ???e ????f?
  s?µß????eta? µe ??a? a???µ? ß?s?? k, 0k-1. ??a
  a?µ? µeta?? d?? ????f?? u, v ?p???e? ?ta? ?a?
  µ??? ?ta?
• 
  ??ad??µ???? t?p??