Abstract

We consider graphs on monomials in n variables of a fixed degree d where two monomials are adjacent if and only if their least common multiple has degree d+1. We find that when n = 3 and d is divisible by 3 as well as when n = 4 and d is even that these graphs have a unique maximum independent set. Domination in these graphs is also considered, and we conjecture that there is equality of the domination number and independent domination number in all cases.

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