论文标题
固定程度的唯一图形中的独特最大独立集
Unique maximum independent sets in graphs on monomials of a fixed degree
论文作者
论文摘要
我们考虑在$ n $变量$ d $ $ n $变量的单元中的图形，当时两个单一元素在且只有其最小常见的倍数具有$ d+1 $的情况下。我们证明，当$ n = 3 $和$ d $可除$ 3 $时，以及当$ n = 4 $和$ d $的时候，这些图甚至具有独特的最大独立集。还考虑了这些图中的主导地位，我们猜想在所有情况下，统治数和独立的统治数有平等。
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 prove 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.
