论文标题
斐波那契运行的图II：度序列
Fibonacci-run graphs II: Degree sequences
论文作者
论文摘要
斐波那契立方体是通过将设置的顶点限制为不包含连续1s的二进制字符串获得的超立方体图的诱导子图。这类图表已经进行了广泛的研究，并在许多不同的方向上进行了概括。在顶点定义斐波那契 - 运行图的二进制字符串上，超立方体的诱导子图引起的子图。这些图的顶点与斐波那契多维数据集相同，但边缘和不同的图理论属性较少。 斐波那契运行的图的基本特性在伴侣论文中介绍，而在本文中，我们考虑了斐波那契 - 运行图的度序列的性质。我们获得的生成函数是对度序列的生成函数的改进，并且具有许多成熟的推论，并作为专业化。我们还获得了被视为部分有序集的斐波那契运行图的几个属性，并讨论了其嵌入属性。
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many different directions. Induced subgraphs of the hypercube on binary strings with restricted runlengths as vertices define Fibonacci-run graphs. These graphs have the same number of vertices as Fibonacci cubes, but fewer edges and different graph theoretical properties. Basic properties of Fibonacci-run graphs are presented in a companion paper, while in this paper we consider the nature of the degree sequences of Fibonacci-run graphs. The generating function we obtain is a refinement of the generating function of the degree sequences, and has a number of corollaries, obtained as specializations. We also obtain several properties of Fibonacci-run graphs viewed as a partially ordered set, and discuss its embedding properties.
