Arithmetic graph: различия между версиями
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'''Arithmetic graph''' | '''Arithmetic graph''' — ''[[арифметичский 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>. | ||
Версия от 11:51, 5 декабря 2011
Arithmetic graph — арифметичский 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].