单圈图斜能量的排序

发布时间：2019-06-10 06:40

【摘要】：图论是一门应用广泛的数学学科,它在自然科学,社会科学等各领域均有广泛的应用.而图谱理论是图论研究的一个重要领域,也是非常活跃的一个研究领域.它在量子化学,物理,计算机科学中都有广泛的应用.图谱理论研究的是图的相关矩阵,如邻接矩阵, Laplace矩阵等的特征值和特征向量及其应用.图能量的研究是图谱理论研究的一个重要应用,在理论化学中有十分重要的应用.特别是图的特征值和共轭碳氢化合物中π-电子的分子轨道能量级之间存在着紧密的联系.对于一个简单无向图G,它的能量E(G)定义为相应邻接矩阵的所有特征值的绝对值之和.自从1977.年著名数学化学家Gutman提出这个概念后就引起很多理论化学家和数学家的广泛关注.进入新世纪后,图的能量更是得到了长足地发展,许多重要结论相继被发现.除了图的邻接矩阵能量,图的其他相关矩阵的能量相继被提出并广泛研究.例如Laplacian能量,Signless Laplacian能量,关联能量,距离能量,定向图的斜能量.类似于无向图的能量定义,定向图的斜能量E(G)定义为定向图的的斜邻接矩阵的所有特征值的绝对值之和.本文通过采用特征多项式的系数比较和函数零点定理的方法来研究定向单圈图斜能量的排序问题和给定围长的定向单圈图的极值斜能量问题.主要结果如下：(1)确定了定向单圈图中第三小到第九小的极小斜能量排序；(2)刻画了给定围长的第二小斜能量的定向单圈图.
[Abstract]:Graph theory is a widely used subject of mathematics, which is widely used in natural science, social science and other fields. Atlas theory is not only an important field of graph theory research, but also a very active research field. It is widely used in quantum chemistry, physics and computer science. The graph theory studies the eigenvalues and eigenvectors of the correlation matrices of graphs, such as adjacent matrices, Laplace matrices, etc., and their applications. The study of graph energy is an important application in atlas theory, and it has a very important application in theoretical chemistry. In particular, there is a close relationship between the eigenvalues of the graph and the molecular orbital energy of 蟺-electrons in conjugated hydrocarbons. For a simple undirected graph G, its energy E (G) is defined as the sum of the absolute values of all eigenvalues of the corresponding adjacent matrix. Since 1977. Since Gutman, a famous mathematical chemist, put forward this concept, many theoretical chemists and mathematicians have paid more and more attention to it. After entering the new century, the energy of the graph has been greatly developed, and many important conclusions have been discovered one after another. In addition to the energy of the adjacent matrix of the graph, the energy of other related matrices of the graph has been proposed and widely studied. For example, Laplacian energy, Signless Laplacian energy, correlation energy, distance energy, oblique energy of directional graph. Similar to the energy definition of an undirected graph, the oblique energy E (G) of the directed graph is defined as the sum of the absolute values of all the eigenvalues of the oblique adjacent matrix of the directed graph. In this paper, the ordering problem of oblique energy of directional unicycle graph and the extreme oblique energy problem of directional unicycle graph with given circumference are studied by using the coefficient comparison of characteristic Polynomials and the theorem of function zeros. The main results are as follows: (1) the order of the minimum oblique energy from the third to the ninth smallest in the directional single cycle graph is determined, and (2) the directional single cycle graph of the second small oblique energy with a given circumference is characterized.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5

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