【作者】 滕海滨；

【导师】 范益政；

【作者基本信息】 安徽大学 ， 基础数学， 2013， 硕士

【摘要】 谱图理论是代数图论的一个重要分支,它主要研究图的邻接矩阵和]aplace矩阵的谱性质与结构性质之间的联系,以期通过图的谱参数来刻画图的结构性质.图的Estrada指数EE(G)定义为其中λ1(G),λ2(G),...,λ。(G)是G邻接矩阵的特征值,是图重要的谱参数Estracla指数源于生物化学领域.2000年,Ernesto Estrada生衡量蛋白质折叠程度时最先引入Estrada指数.随后,由于它在生物化学、信息科学、复杂网络等领域的广泛应用,Estrada指数很快引起了数学工作者的关注.研究者试图通过建立Estrada指数与图的结构参数之间的联系,刻画图的结构性质.众所周知,图的匹配数是图重要的结构参数,在很多方面有广泛的应用.本文讨论了单圈图的匹配数与Estrada指数之间的关系,刻画了含有完美匹配的单圈图中Estrad(?)指数的极大图和极小图,以及具有小匹配数的单圈图中Estrada指数的极大图.本文的组织结构如下.在第一章,首先介绍了Estrada指数的研究背景和意义；其次介绍相关概念,术语和符号；最后介绍了Estrad(?)指数相关的基本结论,研究进展,以及本文的主要研究结果.第二章讨论了含有完美匹配的单圈图的Estrada指数,给出了含有完美匹配的单圈图中Estrad(?)指数的极大图和极小图；第三章研究了小匹配数的单圈图的Estrad(?)指数,分别刻画了匹配数为2和匹配数为3的单圈图中Estrada指数的极大图.更多还原

【Abstract】 Spectral graph theory is an important branch of algebraic graph theory which mainly deal with the relation between the structural property and the spectral property of graphs by using the spectrum of adjacency matrix and Laplacian matrix of graphs.The Estrada index of a graph G is defined as EE(G)=Σin=1eλi(G)which is an important spectral parameter of graphs, where λ1(G).λ2(G),...,λn(G) are the eigenvalues of its adjacency matrix. The Estrada index derived from the field of biochemistry. The Estrada index is an index which was introduced by Ernesto Estrada in2000to measure the degree of folding of a protein. Subsequently, The Estrada index received much attention since it was applied more and more widely in biochemistry, information science, complex network. Investigators try to characterize the structure of property of graphs by creating the relation between the Estrada index and the structural parameter of graphs. As we all know, the matching number of graph is an important structural parameter, which has a wide range of applications in many ways. This dissertation discusses the relationship between the the matching number of unicyclic graphs and Estrada index, characterizes the maximizing graph and minimizing graph among all unicyclic graphs with perfect matching, and the maximizing graph among all unicyclic graph with given small matching number.The thesis is organized as follows. In Chapter one, we introduce the background of the Estrada index of graphs, some concepts and notations which will be used in following Chap-ter. Finally, we introduce the problems, its development and our main results. In Chapter two, we mainly investigate the Estrada index of unicyclic graph with perfect matching, char-acterize the graphs whose Estrada index attain maximum and minimum among all unicyclic graphs with perfect matching, respectively. In the last Chapter, we discuss the unicyclic graph with given small matching number, characterize the maximizing graphs in unicyclic graph with matching number2and in unicyclic graph with matching number3, respectively.更多还原