n条路的笛卡儿积图的匹配排除和条件匹配排除 Alternative Title Macthing preclusion and conditional matching preclusion for Cartesian product of n paths 丁奇 Thesis Advisor 张和平 2014-05-27 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 匹配排除数 匹配排除集 条件匹配排除数 条件匹配排除集 n-grid图 Abstract 本文主要考虑了 n 条路做笛卡尔积之后得到的 n-grid 图的匹配排除和条件匹配排除. 本文主要分为三章。第一章主要介绍了有关匹配排除集和条件匹配排除集的研究背景与研究现状. 第二章主要研究了 n-grid 图的匹配排除数和最优匹配排除集，当 n-grid 图的阶数为偶数的时候, n-grid 图的匹配排除数为 n 且每一个最优排除集都是平凡的; 当 n-grid 图的阶数为奇数的时候，n-grid 图的匹配排除数为 n+1且每一个最优匹配排除集在同构意义下是唯一的. 第三章主要研究了 n-grid 图的条件匹配排除数和最优条件匹配排除集, 当 n-grid 图的阶数为偶数的时候, n-grid图的条件匹配排除数为 2n-1 或者 2n-2 且每一个最优条件匹配排除集都是平凡的; 当 n-grid 图的阶数为奇数的时候, n-grid 图的条件匹配排除数为 2n 且每一个最优条件匹配排除集在同构意义下是唯一的。 Other Abstract In this thesis, we discuss about the matching preclusion and conditional matching preclusion of the n-grid graph which is formed by Cartesian product of n paths. This thesis is divided into three chapters. We mainly introduce the background and research status of matching preclusion and conditional matching preclusion in the first chapter. We research matching preclusion number and optimal matching preclusion set of an n-grid graph in the second chapter. If an n-grid graph has an even order, then the matching preclusion number of the n-grid graph is n and every optimal matching preclusion set of the n-grid is trivial. If an n-grid graph has an odd order, then the matching preclusion number of the n-grid graph is n + 1 and every optimal matching preclusion set of the n-grid graph is unique up to isomorphism. We study conditional matching preclusion number and optimal conditional matching preclusion set of an n-grid graph in the third chapter. If an n-grid graph has an even order, then the conditional matching preclusion number of the n-grid graph is 2n-1 or 2n-2 and every optimal conditional matching preclusion set of the n-grid graph is trivial. If an n-grid graph has an odd order, then the conditional matching preclusion number of the n-grid graph is 2n and every optimal conditional matching preclusion set of the n-grid graph is unique up to isomorphism. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225674 Collection 数学与统计学院 Recommended CitationGB/T 7714 丁奇. n条路的笛卡儿积图的匹配排除和条件匹配排除[D]. 兰州. 兰州大学,2014.
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