论文标题
Eulers Graph World-纯度，规律性和均匀性 - 自然的俗气？ - 构造和示例
Eulers Graph World - Purity, Regularity and Evenness -Law of Nature? - Constructions and Examples
论文作者
论文摘要
我们提出了自然法则？即，纯正的规律性发生在幼稚的水平，规律性与均匀性具有亲和力。在一系列三篇论文中，已经确定只有一种（纯）周期的常规欧拉图不存在。在六种情况之一中，有两种类型的循环的常规欧拉图，即定期的双分部分欧拉图> 2；均匀度在揭示规律性方面发挥作用；最后，K5是一个常规的Euler图，具有三种类型的循环（0,1,3）；这是属性唯一已知的图形；据推测，只有三个周期类型的命令> 5的常规欧拉图不存在，并且在四种情况下的每种情况下，这都是正确的。在（MOD 4）满足相交（组合周期）规则的（MOD 4）下的Euler图给出了一些构造和示例。这些无限类的欧拉图是优雅的候选者。在案例0中呈现了无限的优美图。
We propose a Law of Nature? Viz., Pure Regularity Occurs at Naïve Levels and Regularity has Affinity with Evenness. In a series of three papers, it was established that regular Euler graphs with only one type of (pure) cycles are nonexistent; Regular Euler graphs with only two types of cycles are possible in one of the six cases, viz., regular bipartite Euler graphs of degree >2; Evenness plays role in unveiling regularity; Lastly, K5 is a regular Euler graph with three types of cycles (0,1,3); This is the only known graph with the property; It is conjectured that regular Euler graphs of order >5 with only three cycle types are nonexistent and this is proved true in part cases in each of the four cases. Some constructions and examples are given for the Euler graphs under (mod 4) satisfying intersection (combined cycle) rules. These infinite classes of Euler graphs serve as candidates for gracefulness. Infinite families of graceful graphs are presented in Case-0.
