| Many important structures and properties of graph theory can be described by the eigenvalues and eigenvectors of the correlation matrix of graphs.The topological index obtained by performing some operation on the matrix which related to the molecular graph,it can realize the application of graph in set of real number.Topological index can not only reflect the characteristics of molecular structure,but also reflect the relationship between molecular property and structure.In addition,it can reflect complex physical and chemical properties,etc.In this paper,according to the corresponding matrix eigenvalues of the graph,we mainly study the degree-Kirchhoff index and spanning trees of graphs that based on re-sistive distance.The main content of this thesis is arranged as follows:In the first chapter,we mainly introduce some background and significance of the research,the development of a representative at home and abroad regarding this aspect,and including the main research contents of this paper are also given in this chapter.In the second chapter,we give some necessary definitions,and important lemmas.In the third chapter,we first use the decomposition theorem of normalized Laplace polynomial of a graph,then based on it,explicit closed formula of the degree-Kirchhoff index and the number of spanning trees of On(a linear octagonal chain with n octagonals)are derived,respectively.In the fourth chapter,the main results of this paper are summarized,and on the basis of that,some further research directions are put forward. |
