论文标题
划图图上的素数和复合材料的模式
Patterns of primes and composites on divisibility graph
论文作者
论文摘要
我们研究了无方向性图表，其中顶点集是连续自然数的有限子集，直至N。我们将根据地板函数和除数功能的程度，聚类，地理距离和中心性的测量得出分析表达式。我们讨论了这些度量如何取决于顶点标签和图N的大小。我们还分别呈现了素顶的特定情况，作为推杆。我们可以解释有限尺寸图的局部度量中的模式，以及随着图的大小的增加，全球度量的趋势。
We study the undirected divisibility graph in which the vertex set is a finite subset of consecutive natural numbers up to N.We derive analytical expressions for measures of the graph like degree, clustering, geodesic distance and centrality in terms of the floor functions and the divisor functions. We discuss how these measures depend on the vertex labels and the size of graph N. We also present the specific case of prime vertices separately as corollaries. We could explain the patterns in the local measures for a finite size graph as well as the trends in global measures as the size of the graph increases.
