论文标题
Eulers Graph World-更多关于优雅边界的猜想 - 我
Eulers Graph World -- More Conjectures On Gracefulness Boundaries-I
论文作者
论文摘要
Euler图的特征是每个节点的程度均匀的简单标准。通过限制周期类型，但揭示了Euler图的其他内在特性。例如，在Euler图的εi类中不可能具有高度高于程度的规则性，具有一种类型的循环CN，n = I（mod 4），i = 0,1,2,3。此外，εi中的图是I = 1,2,3的平面。鉴于Euler图的新属性，更优雅的边界是针对Euler图的子类的猜想，并且对于一般图形类别的相关性。在没有一般分析结果的情况下，大部分已发表的论文诉诸证明了无限类别的图表优雅或不合格。本文的目的不是让图形家庭优雅。取而代之的是，根据预期的优雅边界的可用信息，可以指导在哪里寻找优美的图形或导致特征。虽然（Ringel，Kotzig，Rosa）的猜想继续保持不稳定，但此处报道的工作对Rao Hebbare（1975,1981）中所做的猜想进行了更新，随后在Rao（1999,2000）中进行了更多的猜想，基于嵌入的理论和优美的图形，从rao（1999,2000）中进行了优雅的图形。希望这些猜想能够实现建立优雅特性的分析技术。进一步探测了只有两种类型的周期和其他周期组合的欧拉图。
Euler graphs are characterized by the simple criterion that degree of each node is even. By restricting on the cycle types yet additional intrinsic properties of Euler graphs are unveiled. For example, regularity higher than degree two is impossible within the class εi of Euler graphs with one type of cycles Cn, n=i(mod 4), i=0,1,2,3. Further, graphs in εi are planar for i=1,2,3. In the light of new properties of Euler graphs more gracefulness boundaries are conjectured for subclasses of Euler graphs and where relevant extended for general class of graphs. In absence of general analytical results much of the published papers resort to proving an infinite class of graphs graceful or nongraceful. The purpose of this paper is not to give families of graphs graceful or not. Instead, based on the available information expected gracefulness boundaries are proposed which may guide where to look for graceful graphs or lead to characterizations. While the (Ringel,Kotzig,Rosa) Tree Conjecture continues to remain unsettled, the work reported here serves an update on the conjectures made in Rao Hebbare (1975,1981) and more conjectures subsequently made in Rao (1999,2000) based on embedding theorems and graceful algorithms for constructing graceful graphs from a graceful graph. It is hoped that these conjectures lead to analytical techniques for establishing gracefulness property. Further probe into Euler graphs with only two types of cycles and other combinations of cycles continues.
