Arithmetic graph: различия между версиями

Материал из WEGA
Перейти к навигации Перейти к поиску
(Новая страница: «'''Arithmetic graph''' --- арифметичский граф. Let <math>m</math> be a power of a prime <math>p</math>, then the '''arithmetic graph''' <math>G_{…»)
 
Нет описания правки
 
Строка 1: Строка 1:
'''Arithmetic graph''' --- арифметичский граф.  
'''Arithmetic graph''' — ''[[арифметический граф]].''


Let <math>m</math> be a power
Let <math>m</math> be a power of  a prime <math>p</math>, then the '''arithmetic graph''' <math>G_{m}</math> is defined to be a [[graph, undirected graph, nonoriented graph|graph]]
of  a prime <math>p</math>, then the '''arithmetic graph''' <math>G_{m}</math> is defined to be a graph
whose [[vertex]] set is the set of all divisors of <math>m</math> (excluding  1)  and
whose vertex set is the set of all divisors of <math>m</math> (excluding  1)  and
two  distinct  vertices  <math>a</math>  and  <math>b</math>  are  adjacent  if  and only if
two  distinct  vertices  <math>a</math>  and  <math>b</math>  are  adjacent  if  and only if
<math>\gcd(a,b) = p^{i}</math>, where <math>i = 1  \pmod{2}</math>.
<math>\gcd(a,b) = p^{i}</math>, where <math>i = 1  \pmod{2}</math>.

Текущая версия от 16:30, 23 октября 2018

Arithmetic graphарифметический граф.

Let [math]\displaystyle{ m }[/math] be a power of a prime [math]\displaystyle{ p }[/math], then the arithmetic graph [math]\displaystyle{ G_{m} }[/math] is defined to be a graph whose vertex set is the set of all divisors of [math]\displaystyle{ m }[/math] (excluding 1) and two distinct vertices [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math] are adjacent if and only if [math]\displaystyle{ \gcd(a,b) = p^{i} }[/math], where [math]\displaystyle{ i = 1 \pmod{2} }[/math].