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Arithmetic graph: различия между версиями
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Glk (обсуждение | вклад) (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_{…») |
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'''Arithmetic graph''' | '''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>. | ||