本文選題：雙圈圖 + 匹配能量��； 參考：《江西師范大學》2015年碩士論文

【摘要】：圖的匹配能量是由Gutman, Wagner于2012年提出的概念,其定義為圖的匹配多項式的根的絕對值的和.雙圈圖是邊數(shù)等于點數(shù)加一的連通圖.本文分兩部分來研究雙圈圖匹配能量的極圖.1)第一部分得到了給定階的雙圈圖的最大匹配能量的極圖.步驟如下：首先,根據(jù)雙圈圖的結(jié)構(gòu),將其分成兩類；其次,在每類中我們得到了具有最大匹配能量的圖形,也得到了一些更詳細的結(jié)論；最后,我們比較以上兩個極圖并且得到了給定階的雙圈圖的最大匹配能量的極圖.2)第二部分得到了給定階和圍長的雙圈圖的最小匹配能量的極圖.我們采用相似的方法得到結(jié)果.首先,將給定階和圍長的雙圈圖按照以上方法分成兩類；然后得到每一類雙圈圖的最小匹配能量的極圖,同時也得到了一些更精確的結(jié)論,例如將匹配能量變小的一些變換；最后,比較以上兩個最小匹配能量的圖形,我們得到了最小匹配能量的極圖.總之,我們得到了雙圈圖比較匹配能量的偏序并且找到了極圖.
[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.
【學位授予單位】：江西師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O157.5
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本文編號：1800081