邊傳遞Cayley圖的對(duì)稱性研究
發(fā)布時(shí)間：2018-12-31 09:36
【摘要】：圖的對(duì)稱性研究是一個(gè)比較活躍的研究領(lǐng)域,其主要研究對(duì)象是點(diǎn)傳遞圖、邊傳遞圖等具有較高對(duì)稱性質(zhì)的圖.研究某種具有對(duì)稱性質(zhì)的圖有重要的理論意義.在圖的對(duì)稱性研究中,確定圖的自同構(gòu)群是具有基本重要性的工作.如果圖的自同構(gòu)群在圖的頂點(diǎn)集、邊集或2-弧集上作用傳遞,則稱圖分別為點(diǎn)傳遞的、邊傳遞的或2-弧傳遞的.本文的主要研究對(duì)象是具有邊傳遞性質(zhì)的Cayley圖.本文的主要工作是研究無平方因子階的局部本原圖和本原2-弧傳遞圖的對(duì)稱性.首先,本文通過考察圖的自同構(gòu)群某個(gè)最大正規(guī)子群在其頂點(diǎn)集上的軌道情況,得到了無平方因子階局部本原圖及其自同構(gòu)群的簡單刻畫.其次,本文通過對(duì)有限群的子群結(jié)構(gòu)和圖自同構(gòu)群的點(diǎn)穩(wěn)定子分析,構(gòu)造滿足條件的相關(guān)圖類,得到了無平方因子階本原2-弧傳遞圖的分類與刻畫。
[Abstract]:The symmetry study of graphs is an active research field. The main research objects are vertex transitive graphs, edge transitive graphs and other graphs with higher symmetry. It is of great theoretical significance to study some graphs with symmetric properties. In the study of graph symmetry, determining the automorphism group of graphs is of fundamental importance. If the automorphism group of a graph is transitive on the vertex set, edge set or 2-arc set of a graph, then the graph is point-transitive, edge-transitive or 2-arc transitive, respectively. The main research object of this paper is Cayley graph with edge transitive property. The main work of this paper is to study the symmetry of local primitive graphs and primitive 2-arc transitive graphs of square free order. Firstly, by investigating the orbit of a maximal normal subgroup on the vertex set of a graph, we obtain a simple characterization of the square free order local primitive graph and its automorphism group. Secondly, by analyzing the subgroup structure of finite groups and the vertex stability subgroups of graph automorphism groups, we construct the classes of correlation graphs satisfying the conditions, and obtain the classification and characterization of primitive 2-arc transitive graphs of square free order.
【學(xué)位授予單位】：安徽工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5
[Abstract]:The symmetry study of graphs is an active research field. The main research objects are vertex transitive graphs, edge transitive graphs and other graphs with higher symmetry. It is of great theoretical significance to study some graphs with symmetric properties. In the study of graph symmetry, determining the automorphism group of graphs is of fundamental importance. If the automorphism group of a graph is transitive on the vertex set, edge set or 2-arc set of a graph, then the graph is point-transitive, edge-transitive or 2-arc transitive, respectively. The main research object of this paper is Cayley graph with edge transitive property. The main work of this paper is to study the symmetry of local primitive graphs and primitive 2-arc transitive graphs of square free order. Firstly, by investigating the orbit of a maximal normal subgroup on the vertex set of a graph, we obtain a simple characterization of the square free order local primitive graph and its automorphism group. Secondly, by analyzing the subgroup structure of finite groups and the vertex stability subgroups of graph automorphism groups, we construct the classes of correlation graphs satisfying the conditions, and obtain the classification and characterization of primitive 2-arc transitive graphs of square free order.
【學(xué)位授予單位】：安徽工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5
【參考文獻(xiàn)】
相關(guān)期刊論文 前6條
1 徐尚進(jìn);張躍峰;曹夢(mèng)月;;pq階正規(guī)邊傳遞Cayley圖[J];廣西師范學(xué)院學(xué)報(bào)(自然科學(xué)版);2015年03期
2 Xiao-hui HUA;Shang-jin XU;Yun-ping DENG;;Tetravalent Edge-transitive Cayley Graphs of PGL(2, p)[J];Acta Mathematicae Applicatae Sinica(English Series);2013年04期
3 徐尚進(jìn);劉翠明;康U，
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