Arithmetic graph

Arithmetic graph — арифметический 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].