论文标题
在单移民$ 3 $ - 级别的半径上
On unigraphic $3$-polytopes of radius one
论文作者
论文摘要
我们询问哪种程度序列在$ p $ Vertices上作为$ 3 $ - 多层图（Polyhedron）的独特认识。我们给出了这些序列的详尽列表，即一个程度等于$ P-1 $，而两个或三个等于$ 3 $。我们还通过开发快速算法并利用高性能计算，找到了所有$ 3 $ - 级别的半径radius One，以及$ Q \ leq 41 $边缘的所有$ p \ leq 41 $边缘。
We ask which degree sequences admit a unique realisation as a $3$-polytopal graph (polyhedron) on $p$ vertices. We give an exhaustive list of these sequences for the case where one degree equals $p-1$ and exactly two or three of them equal $3$. We also find all $3$-polytopes of radius one with $p\leq 17$, and those with $q\leq 41$ edges, by developing a fast algorithm and making use of High Performance Computing.
