双圈图的匹配能量

发布时间：2018-04-25 06:10

  本文选题：双圈图 + 匹配能量　； 参考：《江西师范大学》2015年硕士论文

【摘要】：图的匹配能量是由Gutman, Wagner于2012年提出的概念,其定义为图的匹配多项式的根的绝对值的和.双圈图是边数等于点数加一的连通图.本文分两部分来研究双圈图匹配能量的极图.1)第一部分得到了给定阶的双圈图的最大匹配能量的极图.步骤如下：首先,根据双圈图的结构,将其分成两类；其次,在每类中我们得到了具有最大匹配能量的图形,也得到了一些更详细的结论；最后,我们比较以上两个极图并且得到了给定阶的双圈图的最大匹配能量的极图.2)第二部分得到了给定阶和围长的双圈图的最小匹配能量的极图.我们采用相似的方法得到结果.首先,将给定阶和围长的双圈图按照以上方法分成两类；然后得到每一类双圈图的最小匹配能量的极图,同时也得到了一些更精确的结论,例如将匹配能量变小的一些变换；最后,比较以上两个最小匹配能量的图形,我们得到了最小匹配能量的极图.总之,我们得到了双圈图比较匹配能量的偏序并且找到了极图.
[Abstract]:The matching energy of a graph is a concept proposed by Gutman Wagner in 2012. It is defined as the sum of the absolute values of the root of the matching polynomial of a graph. A bicyclic graph is a connected graph in which the number of edges is equal to the number of points plus one. In this paper, we study the polarity graph of matching energy of bicycle graph in two parts. In the first part, we obtain the polar graph of the maximum matching energy of bicycle graph of a given order. The steps are as follows: first, according to the structure of bicyclic graph, we divide it into two categories; secondly, we get the graph with the largest matching energy in each class, and get some more detailed conclusions. We compare the above two polar graphs and obtain the polar graph of the maximum matching energy of a bicycle graph of a given order. In the second part, we obtain the pole graph of the minimum matching energy of a bicycle graph with a given order and girth. We use a similar method to get the results. Firstly, the bicyclic graph with given order and girth is divided into two classes according to the above method, then the pole graph of the minimum matching energy of each type of bicycle graph is obtained, and some more accurate conclusions are obtained, such as some transformations that reduce the matching energy. Finally, by comparing the two graphs of the minimum matching energy, we obtain the pole graph of the minimum matching energy. In short, we get the bicycle graph to compare the partial order of matching energy and find the polar graph.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5
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本文编号：1800081