一些 Randic 指标上的新证明与结论 Alternative Title Some new proofs and conclusions on Randic index 郭放 Thesis Advisor 张和平 2012-05-27 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword Randic 指标 广义 Randic 指标 多边形系统 Abstract 第一章中, 首先介绍Randic 指标的化学背景和研究进展，然后是用到的基本定义，概念，和记号，最后总结文章的主要工作。 第二章中,我们讨论Randic 指标的另一种形式对于计算和极值问题的意义，基于它得到一些结果，其中用新的思路重新简化地证明了n 阶的一圈图中Randic指标的极小值问题。 第三章中, 我们先讨论具有 h 个六边形的六边形系统的极值问题,证明了极大值的确界，并且刻画了极值图。在此过程中我们重新简单地给出六边形系统的Randic 指标的计算表达式。对于最小值问题，我们刻画了一些极值图的性质，并且给出了关于螺旋序列的猜测。最后我们讨论了渺位多边形系统的广义Randic指标，这类图包含了cata型苯系统以及亚苯基系统。我们给出了它的广义Randic指标的表式，并用它来证明一些结论和求解极值问题。 Other Abstract In the ¯rst chapter, we introduce chemical background and research progress about Randic index, and then the basic definitions, concepts, and notations, at last the main work in this paper. In the second chapter, we discuss the meaning about another expression on Randic index for calculations and extremum problems, we get some results basedon it, including a simple proof of minimum problem about unicyclic of order n by using a new idea. In the third chapter, we discuss the extremum problem on hexagonal system, and prove that the supremum, also depict the extremal graph. During this process we re give the calculation expressions of Randic index on hexagonal system simply. For the minimum problem, we characterize some properties of the extremal graphs, and give a conjecture about the spiral sequence. Finally, we discuss the catacondensed polygonal system generalized Randic index, this classcontains catacondensed benzenoid systems and the phenylenes. We give a expression of general Randic index about this systems, and prove some conclusions and solve extremum problems by using this expression. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224426 Collection 数学与统计学院 Recommended CitationGB/T 7714 郭放. 一些 Randic 指标上的新证明与结论[D]. 兰州. 兰州大学,2012.
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