3 problems

For positive integers $n$ and nonnegative integers $d$, let $G_n(d)$ be the graph whose vertices are the monomials of degree $d$ in $n$ variables, with two monomials adjacent exact…

For positive integers $n$ and nonnegative integers $d$, let $G_n(d)$ be the graph whose vertices are the monomials of degree $d$ in $n$ variables, with two monomials adjacent exact…

Let $G_3(d)$ be the graph on the monomials of degree $d$ in three variables, with two monomials adjacent exactly when their least common multiple has degree $d+1$. Let…